ibiz
General performance tips apply here as well.
How large are your Spriter files?
Each of them will consume memory. For the same reason you don't want highest resolution images & top-quality sounds in your game, you should avoid using large Spriter files. Try to avoid creating repetetive animations & use as less bones as you can.
How large are your bones? (awkward)
Bones are only Sprites with images. Larger images - more memory is wasted.
Which method of export to use?
If you need better optimization and your bones should have from little to zero customization - use individual sprite export method. (See more on the first page of this topic)
If you're making game for desktop/consoles or want some customization - use each bone as individual sprite. (Check videos on youtube)
That's it -_-
So the short answer: Yes, number of bones affects the performance.