Here's some comments about the accelerator pump and the "small metal bearing" that the OP saw fall out.
I've written about this several times before and it's no big deal but just FYI for anyone interested.
The accelerator pumps on these Keihin BJ and BG carburetors are totally useless junk.
To repair the pump you have to replace the carb bowl and piston but you will get nothing in return for the effort.
That little "small metal bearing" is the pump supply charge check ball. It comes with a new float chamber captured in it's seat with a crimp. So, if it is rolling around loose, it has failed and all the pump will do when stroked is push fuel back into the main chamber. I can't remember ever finding one still captured in it's seat on any carb I have disassembled. It cannot be repaired to my knowledge.
No matter though because the pump piston and bore will be found to be worn out anyway. Trying to "shine" them up won't work and new parts is the only "repair" possible. But, like I said before....no return on investment. You won't notice a lick-O-difference after doing so.
Well, Ok...if you HAMMER the throttle....IMMEDIATELY after putting in a new one you MIGHT see a wee bit of difference. But...that will only last for a very short time since I don't think it's an exaggeration to say this piece of crud pump assembly starts falling apart almost instantly after first use.
I have actually removed the piston and spring in them for customers on several outboards and no one can tell the difference in performance.
And THAT'S JUST WIERD too!
Because....
....if the accelerator pump nozzle gets even a little bit plugged up...
...there can be ALL sorts of problem symptoms!
From hard start, stalling and low power!
WHY?
I am not really sure!
It's as if this carb can't BREATHE correctly if that pump nozzle isn't fully open.
To sum up...
Keep the dust bellows boot fresh to keep out dirt.
If you find a worn piston or bore, don't worry too much about it UNLESS it's cocking so badly in the bore it's seizing and not letting the linkage travel freely.
(Even then, no big deal...the linkage is spring loaded and will still work)
And, if you find that little ball rolling around loose or it falls out and goes down a crack, just shrug and move on.
But KEEP THAT NOZZLE CLEAR!
These things should have never been added to these otherwise pretty great little carburetors.