If the mod simply adds one of the bows that can normally be found in the game, it will stay.
If the bow is exclusive to the mod, then the bow will disappear and you will have to find it again.
You may also have to deal with a very small added amount of savegame bloat, which will carry forward. To put it basically, that's because you accessed an inventory item that then was removed, while the ID for it still exists in Oblivion. If it happens once or even a few dozen times, it's no big deal, but if it happens a lot, it can add to game instability. Some of us have been known to add plenty of mods and really enjoy collecting items (cough), so that can become an issue if one isn't careful, and works around it.
That's why it's probably a good idea to buy an in-game garbage can or item with similar functionality. The idea is that when you plan on removing a mod, you feed all the items you've picked up from that mod into the can. It not only deletes them, but all references to them from within the game. No bloat.