Steve's certainly right about using the proper voicings, focusing on the D and G strings, and using a loud acoustic archtop with heavier strings. And I do what I can to preserve the natural acoustic balance of 1930's-1940's music. I actually don't play anything except 30's and 40's stuff, so I really aim for a pre-bop feel for everything, rhythmically, harmonically, sonically, etc.
That said, unless I'm playing in a really well designed acoustic space, I need a little help. Plus, not everyone has sidemen with similarly period correct gear, and as Michael at
www.FreddieGreen.org has written, the sonic properties of amplified bass and modern cymbals and drum heads are just not the same as old ones. Almost all of my gigs involve bass players with gut strings, vintage drum sets and cymbals with calf or at least calf-substitute heads - and it's a whole different thing. You might not be so lucky. And even if you are, you might still appreciate a little boost.