If YOU really want to, go get an acoustic bass guitar. But, in my experience, a nice warm sounding electric fits just fine.
Whenever I'm playing an acoustic set, I play MUCH more laid back, I pluck closer to the neck than I usually do, and on my Jazz basses I'll favor the neck pickup and roll the tone down. Works like a charm.
In my experience, I've never been able to justify for myself the purchase of an acoustic bass guitar (no matter how many times I try). They seem like one-trick ponies that need to be plugged in anyway to be any kind of useful, and if I feel like my Jazzes (or my fretless) can cover just about anything I want, why would I get anything else?
Again, just my opinion.