While doing my random theory crafting about a support/control I've been wanting to make, I settled on bard, lore bard, because lore bard, but then I was thinking about what else I could do and Divine soul sorcerer popped into my head for access to more spells and other things. Does this seem viable?

It depends on how many levels you plan to put into each.

The problem comes from the multiclass spellcasting rules. You can only know and prepare spells for each class as if they were single leveled in those classes - but your spell slots will be that of a full caster (as Bard and Sorc are both full). So if you decided to go half and half - you would be able to cast using high level spell slots but you would only know a load of low level spells.
Typically for full casters you play them to get access to the highest level spells so you'd be shooting yourself in the foot by doing this. For this reason alone I don't recommend it.

As for the abilities of each class/subclass I can't really comment. I've never played a Bard so I have no idea how it would pair with a Divine Soul Sorcerer.

Edit:
Also - the Bard spell list is already very versatile - so branching out to get access to the Sorcerer and Cleric spell lists really wouldn't offer you very much - especially not for the cost.

You'd get more Cantrips - but if that was your plan - you'd probably be better off just getting the Magic Initiate feat instead.

My Whispers bard did take a 1 level dip into Divine Soul and it’s not bad. I don’t know if I would do it again, but it’s not the worst decision in the world. I have a ton of cantrips, but aside from the utility ones (which I use a lot,) the only cantrips that get used often in combat are Vicious Mockery and Chill Touch. Gaining more lower level spells known wasn’t bad though, it let my focus my Bard Spells on interesting stuff (like Enthrall) because the Divine Soul got me the extra healing spells, and being able to shake a bad guys hand and hit them with a 3rd-level Inflict Wounds when they least expect it is always fun too.

I'm playing exactly this right now in an Out of the Abyss campaign. She's a ton of fun, but at level 11, she doesn't hit as hard as the other members of the party. The spell selection is nice, especially being able to pump 3rd level spells up to 6th without having to worry about losing out on casting something more powerful later. I am kinda at the point now though where I am probably going to leave one where it is and level the other exclusively. Just haven't decided which. 

Oh... and having silent spell as a Bard for social encounters is pretty amazing.

I see. I think I may do it then, though idk what I should put int each. How are you splitting it?

Right now she's a 6 Bard/5 Sorc. I'm leaning towards going all Bard the rest of the way. If she ever does get to 20, that'll give her access to 8th level spells, which would be unobtainable if I went sorc. Of course, I'm doubting we'll hit 20, but you never know. There're just too many good things in the 10-15 range for me to pass up in Bard, and it goes with her concept. 

Possibly, but you can just get the spells you want through magical secrets anyway.

I was thinking Spirits Bard with Divine Soul Sorcerer any thoughts?

Quote from jayjoylove >>

I was thinking Spirits Bard with Divine Soul Sorcerer any thoughts?

 
I recommend not taking more than 2 levels in Sorcerer at most, and then taking the Metamagic Adept feat. Otherwise you give up too much Bard stuff and bards are too cool.

I feel you! I was thinking of starting as Sorcerer, then focusing on Bard from lvls 2-7, then maybe back to Sorcerer. The College of Spirits and Divine Soul tie in well together thematically for the idea of the character in general. Thanks for the input!

Monk and sorceror with their Ki and sorcery points are difficult classes to multiclass into or out of.  Bards are another class that gets something good at almost every level so while it can be made to work and work well, it takes a lot of planning and effort to do so.