I play my bass through any amp that happens to be handy. Don't worry about it. The newer bass amps have their tone controls tailored for bass, but the older ones were'nt much different at all.

The main difference is that it takes more power to produce a given sound level at bass frequencies. The ultimate tube bass amp was (is) the Ampeg SVT 300 W amp. My favourite guitar tech has one that he uses for guitar sometimes. It sounds awesome!