How to reset the inventory of a merchant via console

Expanding on my comment that there is no way to search for an item in the game*.

One answer is to use console commands to add the bow to a known merchant then manually buy back the bow from the merchant. You might want to do this with a merchant who is likely to have acquired the bow naturally though any merchant will do.

First you will need to find out what the FormID of the bow is. To do this you will need to load a previous save where you have the bow. Open the console and run:

ShowInventory

The bow will be listed with it's FormID being enclosed in brackets after the name.

1 - Item Name (FormID) (other stuff)

(I think you can also just drop the bow and left click on it?)

After you know the FormID load up your current save game and find the merchant you want to give the bow to. Open the console and left click the merchant, running:

AddItem FormID

Close the console and buy the item from the merchant as normal.

If you ever encounter the "real" bow then you should remove this from the game by selecting the merchant and running:

RemoveItem FormID

*The toolkit or a custom mod may add this, however they are not released as of this post.

I've had success with a few things when it comes to people following me. I'm not on a sneaky character, so I've had to get crafty for some missions. It sounds like you've tried some of these methods already, but I'll put them here anyway just for completion's sake.

One is to try during the day, when people are out and about or tending to their stores. I've noticed that some (not all) vendors will stay at their counters instead of following me.

Second, is to go in and scout a quick path while letting the person follow you, but not steal anything. Then, go out and come back in (this usually resets their position) and make a mad dash for whatever you needed to get. I may just be lucky at encountering slow people, even in Solitude. I'm not sure if their speed or concern with me stealing something is related to anything.

Finally, I've also had success with telling my companion to wait on the stairs or in smaller door ways to block the person from following me, or at least slow them down more. It seems to be hit and miss, but it's worth a try.

I've also read (and it's mentioned in a comment above) that buckets/pots on heads can work. I've never tried it myself, but it would be a lot funnier than any of my suggestions! Maybe some combination of buckets and companion blocking to slow them down would help.