I'm currently playing a Drow Rogue 7 and just added a level in Bard (so total level 8). Currently my Roguish Archetype is Thief, but it doesn't quite fit my character, and I'm playing in a homebrew campaign with an emphasis on roleplay so I'd prefer something more fitting to my character. That being said, while roleplay is a slightly higher priority, I can't afford to be dead weight in combat either. I've been eyeing Swashbuckler but I'd like to weigh the benefits of it vs Thief as well as in conjuction with my future Bard subclass before I make any purchases.

As for my Bard subclass, I'd really like to go with the College of Eloquence as I feel it suits my character the best, but I want some opinions on how well it would mesh with Swashbuckler. It's very important that I have access to healing, as the rest of my party consists of a Fighter/Rogue Assassin, Monk, and a pure Rogue who happens to have a very low CON. (The other Rogue is currently Thief but plans to change to Arcane Trickster.) So as you can see we really needed the variety as we have a lot of Rogues and no healer. Oh, and our Monk was recently partially petrified, so if it is at all possible to gain access to a spell that can cure it would be awesome.

I haven't yet decided how many levels I want to advance in either class, mostly because I don't know which skills are more valuable from Swashbuckler or College of Eloquence, and with the latter being so new I don't know how all of the skills actually work. Sorry if this is more information that needed, but I'd really appreciate some advice from more experienced players.

I would say that you should go lore bard. That way you can get magical secrets earlier and get expertise in medicine. That way you don't always have to go for spell slots. Ask the other rogue why they're going arcane trickster, when you are going bard? 

Or you could ask to remake your character.  Go Bard and that way your party is more balanced. I would still say lore bard. Greater restoration should work. 

I'm not interested in going full Bard specifically for roleplay reasons, it doesn't really suit my character so she needs to at least stay where she's at in Rogue, and picking Swashbuckler would give me quite a bit of variety from Assassin and Arcane Trickster. I'm already level 1 in Bard and have proficiency in medicine, and expertise is available at 3rd level regardless of college so I should still be able to get that expertise after 2 more Bard levels. Otherwise Magical Secrets (at level 6 for all colleges, I thought) and Greater Restoration are available to all Bards, so I don't see why I should need to go Lore for that?

No. Magical secrets at level 6 is only lore bard, the rest get it at 10, 14 and 18 (lore bards get it as well, just that they get extra). I guess then swashbuckler works, or maybe inquisitive or mastermind? They both allow you to play a different rogue. 

While Magical Secrets would be useful I don't know that I'd really need it badly enough at level 6 (and honestly I'm not certain that I will even reach that level before the campaign ends) to warrant going Lore. Besides that, I use persuasion pretty often, so Eloquence's Silver Tongue would probably be more useful to me. Mastermind doesn't really fit my character either, although Inquisitive could definitely be viable if I didn't already have expertise in insight that it doesn't feel as useful. I think Swashbuckler benefits the most from putting more charisma in for Bard anyway.

I've built a support rogue/bard by going 7 mastermind/3 lore bard.  6 skills with expertise, 7 tool proficiencies (1 gaming set, 1 instrument, alchemist supplies, poisoner's kit, disguise kit, thieves tools, forgery kit.) 11 with proficiency total, and half proficiency in everything else.  Alert feat and a weapon that gives +2 to initiative, so he's +12.  The strategy with him is using his bracers of flying daggers for 2 thrown dagger attacks + sneak attack.  Then  throwing out a bonus action every turn to help allies, bonus action healing word when someone drops, cunning action if he needs to bolt or hide, and cutting words as a reaction to help allies from being hit.  It's a very fluid action economy and in combat he's no slouch with 2D4 + 4D6 + dex to his damage.

Sword bard/Swashbuckler is a fun combo from what I've seen.  The abilities benefit both classes by giving swashbucklers more maneuverability in combat and an extra benefit to their attacks with a fighting style (Dueling for +2 to damage with a 1 handed weapon only, or two-weapon fighting to add your mod to your bonus action off hand attack) and flourishes. 

I can see sword bard working with thief well because one of the blade flourishes allows you to push an enemy away from you.  In theory you could bonus action sleight of hands to steal their weapon, attack them and push them 5 feet from you, then run away.

Glamour bard would work well as their bardic inspiration can be used to allow your allies to reposition themselves on the field if they get themselves in a sticky situation.  And if you're doing the party's persuading enthralling performance can be handy.  At higher levels mantle of majesty can give you almost total control of a combat.

Valour bards give the rogue proficiencies in all martial weapons and medium armor (Hello longbow and half plate!) and their bardic inspiration is excellent for offensive/defensive purposes.  Adding an extra die roll to damage or to an ally's AC can be the difference between a party wipe and a party win. 

If you're less interested in the other bardic ribbons, then look no further than Whisper bard.  Their bardic inspiration psychic blades works pretty much the same as sneak attack.  Mantle of Whispers is great for infiltration, and words of terror is a really fun ability to use.  My DM knows when my, "Look at me, I'm the captain now!" moments are coming at this point.  My whisper bard is level 16, has the bracers of archery (for longbow proficiency) and an oathbow and the sharpshooter feat.  He's able to drop 8D6 psychic blades in a single attack and is essentially a rogue with 8th level spell slots. Cast swift quiver, then each turn fire off 2 arrows for lots of damage.

I really appreciate your detail, but I meant I was looking for info on College of Eloquence, not that I was still deciding on a Bard class. Do you know how well that would work with Swashbuckler?

College of Eloquence is... it's very good in general. And there are things that work well with Swashbuckler, like the ability to treat any persuasion roll as at least a 10. But the rest of abilities don't dovetail as nicely. Especially the ability to use a bardic inspiration to reduce an opponent's saving throw roll. Nothing about swashbuckler calls for saving throws, so it kind of defeats the purpose. 

Honestly, if you're going swashbuckler, Valor is probably the best bet. Nothing about Valor bard says you can't still take/cast healing spells, but now you can augment your damage output, get extra attacks, etc. Failing that... I hate to revisit a sensitive topic, but lore bard also has Cutting Words, which can weaken opponents' ability to resist the swashbuckler abilities, and the extra spells can be revivify or big party heals from the cleric and druid lists. 

I also greatly enjoy my scout rogue. The extra skill and expertise are awesome.  Plus with warlock you can get devils sight. Then have mage cast darkness in front of you and cut them up with your daggers