Well, I really love Billy, so I don’t mind Bill! Actually I think I prefer it over Will (Will feels really worn out at this point imo).
I’m not sure about Bob though. But since you made me imagine it on a little boy it’s not toooo bad…kinda playful maybe? I could come round to Bobby even.
My favorite thing about both names though is that they’re really reminiscent of the 1920s & 30s! Bill especially makes me think of a 1920s college football player who dates girls with names like Flo, Hazel, Gladys and Pearl :D