No thanks pal! When guys come up to me at a gig and ask to play a song I usually say "I guess so, where is your bass?"
They then say, "oh, I don't have it with me now, it's home". Then I say "Oh, too bad we will probably be done with the gig by the time you go get it and return."
Bada boom.
Here's the sad truth. And, right up front, I know I'm generalizing here. But, as is often the case when I generalize, I don't care.

(Stole that from Dave Barry.) But seriously...
Any cat who actually asks to sit-in just doesn't get it. The only exception here is when he does have his instrument with him, but at that...he only asks after establishing a solid rapport with you, and with the bandleader. Otherwise, "Can I play...?" is rude, clueless, and lets you know that you're not dealing with a pro.
Us bass players are, by and far, pretty damn awesome. We'll invite a guy to sit in, if (a) we have a good feeling about him, (b) the situation is right - maybe he's new in town and is networking to establish himself - and most important, (c) the gig allows for it and the bandleader is comfortable with the situation. All of that involves two-way communication and requires the proper etiquette on both ends.
Bottom line - unless you know the invitation has already been implied, wait for it to come verbally. Personally, I love it when friends/cronies stop by...and they will be asked to play.
Side note....how to get that invitation from a Roscoehead:
- Comment on the last set. "Man, I loved that flat-six-five turnaround on that blues. You really made the guitarist sound good during his solo."
- Introduce yourself with a goal in mind. "You guys sound great, and this seems like a cool gig. I just moved here from Blacksburg (don't mention that you got run out of town by a bad-ass 'slinger with Joe Bardens in his holster) and am looking for work."
- And of course, comment on the Roscoe. "That is a beautiful bass, and I really dig the music you're making with it. Is that koa?"
