While I'm relatively new (to bettas, not fishkeeping in general, but you may want to wait for a more experienced member to help you) I believe a 2 gallon bowl cannot hold a stable cycle, especially if unfiltered (do you have a filter in it at all?).
If you don't have a filter you'd need to do regular 100% water changes, so a cycle wouldn't be able to establish itself as the water is consistantly being changed.
Even with a filter I'm not sure if a 2 gallon bowl can maintain a stable cycle, so I wouldn't think you'd have any problems with cleaning the bowl and ornaments, refilling it and then acclimatising the fish back to it.
If you have substrate (gravel, rocks, whatever) in the bowl I suggest thoroughly rinsing that with hot water as well just in case there is something nefarious residing in it.