As we read the current rules, and since dropping a weapon now is just as time consuming as properly sheathing it, there is a really weird mechanical effect. It is awkward, complex, unsatisfying and doesn't match with common sense at all. We had this come up in our session last weekend. And I *think* I know how the rules are maybe hoped to interact, but it's not spelled out clearly.

A gnome ranger is really set up to be a two-weapon fighter, but he does often use his shortbow to start an encounter. He has two attacks a round naturally. Something closed with him faster than expected. He was ready to use all his two-weapon goodies, but couldn't.

He started his round with his bow in hand. In the past, we would have let him drop the bow for free, then use his feat to simultaneously draw both weapons and go to town. But dropping an item isn't free now. So it played out a bit differently as we were trying to quickly parse the rules accurately in the middle of a fight.

First attack, he let's the bow stay in his left hand and draws his shortsword with his right hand to make the first attack. (Already, he can't take advantage of one of his feats to draw two weapons since dropping a bow now costs the same as putting it away.) He makes his second attack with the shortsword in his right hand which allows him to stow the bow, but he doesn't have a second weapon in his left hand to allow the bonus attack at this point.

At the moment, we read it as you have to have a weapon available to make the attack with to even qualify for the Bonus action, but it's possible that the better read is that you are qualified for the Bonus just by making an attack with a light weapon, whether you are set up for it or not. So in the moment it was ruled that he couldn't make the off-hand Bonus attack this round. However, had he taken the previous round to draw his bow on the first attack, make the second attack and then stow it, he wouldn't run into any issues whatsoever.

I guess the real point of this is that making dropping something not be a mindless free thing just feels like an unnecessary change that doesn't add anything to the game and at best mucks things up. (We can argue all day about the practicality of sheathing and unsheathing weapons as the game allows, but I think it feels pretty obvious that it's always going to be way faster to open your hand and drop something rather than putting it back properly.)

Unless I've missed something in the new rules, you can only draw OR stow the bow in your turn.  You wouldn't be able to draw the bow, make two ranged attacks then stow/sheath/shoulder it (or drop it).

I'm not sure what you have on the character but I'm guessing its the Dual Wielder feat.

• You can draw or stow two one-handed weapons when you would normally be able to draw or stow only one.

Unfortunately the Shortbow is a two-handed weapon so the Dual Wielder feat won't help you stow it with one hand and draw a weapon with the other.  Nor can you stow it and draw a weapon with the same hand in the same turn.  I think you made the right call.  Best to keep the bow held in one hand and draw a shortsword on the first turn.  Next turn you stow the bow and make another attack with the shortsword.  Third turn you can draw the second shortsword and use it with the bonus action.

Because the Dual Wielder feat lets you attack with a non-light weapon in your off hand, a reasonable DM might let you wield the bow as an improvised weapon.  Unless you have the Tavern Brawler feat you wouldn't be able to use your proficiency on the attack roll.

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Note that dropping a weapon was never really a free action RAW.  It just wasn't noted as part of the object interactions and when Devs were queried on it they said they would allow dropping a weapon for free.  The problems this led to are  a number of shenanigans around being able to drop a weapon, do some other action with your free hand, then pick the dropped weapon back up, in the same turn.  There was a recent discussion about the Soulknife rogue's Psychic Blades on the problems of them being unable to use them for Opportunity Attacks or have another weapon ready for Opportunity Attacks if they wanted to make the Bonus action Psychic Blades attack.  Until someone pointed out that RAW (along with the Dev Tweet) you could hold a polearm or great weapon, drop it, make the Psychic Blades attacks then pick it back up and have a Reach or Great weapon ready for Opportunity Attacks.  The same would occur for casters who might need a free hand for a Somatic spell as they held a shield on one arm and a weapon of focus in the other, they'd drop the weapon/focus, cast the Somatic spell and pick it back up in the same turn.

So to bypass those shenanigans they have specified that dropping a weapon is now equivalent to stowing or drawing it and done away with these strange moves.  Consider that this is playtest drafting so they might be testing so see what people think of it.

However, another part of me thinks that you can't have your cake and eat it.  You've tried to setup a character to attack from range to begin with then switch around their weapons when they're engaged in melee.  Really, its an attempt to have the best of both worlds between ranged and melee rather than be setup in advance for one or the other.  One immediate benefit I see is that it might encourage usage of thrown weapons since they are often both melee and have the benefit of range.  Obviously, this makes the player more limited at range since thrown weapons often have much shorter range and leave the player bereft of the weapon they've just thrown, but it feels more balanced than being able to use the best weapon for range and following on with the best weapon setup for close quarters.  Another example might be using a bow but drawing a longsword if the opponent closes the gap.  They can't use the versatility characteristic of the longsword since they still hold the bow, but they only put up with it for one turn before they can drop the bow and wield the sword with both hands.  Although archers are more likely to have good dexterity and wield a rapier anyway.

An alternative to forgoing the drop weapon usage of free interaction, might be to add the ability to shoulder a bow and draw a weapon in the same turn as part of a feat which would be attractive to archers who may wish to switch to melee if an opponent closes.

I think you are misreading the Equipping and Unequipping Weapons section.  You can either equip or unequip one weapon when you make an attack as part of this action. You do so either before or after the attack.

You can just start with short bow in your hands.  Make 1 attack with the shortbow and then stow it after,  Before your second attack draw your 2 shortswords.  Then make your attack and off hand attack.