There was an article circulating years ago about tightbores...basically a "what's it about and how tight is too tight accuracy vs. FPS".
Re. the OP question...first you'll need to know what the inner of the existing barrel is. If it's 6.03/6.04 already...switching to a 6.03mm tightbore may not do anything at all. From that article and some other observations tighter than 6.04mm and you start to see drop off in FPS (again, I doubt you'll see 20+ FPS drop) and higher rates of jams.
The "old" guestimates was that going from a 6.08mm barrel to a 6.04mm barrel would net you ~7-15ish FPS.
The ONLY way to tell is to use a chronograph.
Re. the bouncing thing...I'm sure there are bounces in the barrel...and I certainly hope it's not more than 2, one right after/at the hopup and another partway down the barrel (at worst). The projectile is traveling a fairly short distance at relatively high speeds...carried by a cushion of air.
If the BB bounced multiple times down the barrel you'd see highly variable hopup application and significant FPS losses. If it "spiral-bounced" down the barrel you'd see shots all over the place (akin to when guys have their hopup nubs set off center or jammed in crooked).