Early Bass guitar players didn't have a lot of choice when it came to amps. They simply plugged into what was available. (Which was pretty much the same stuff that was available for guitar players.) It didn't take long for everyone to realize that the bass guitar had it's own special needs when it came to amplification, and that amps designed for guitars were just not going to cut it.

Bass guitar amps require a different design approach than guitar amps. The lower frequencies that need to be reproduced require heavier duty speakers, (often in larger sizes) and lot's of power.

There are basically three different types of bass amplifiers:

Tube or Valve amplifiers: The original amps used since the dawn of electric guitars. Tube amps, by the nature of their technology, introduce a warmer, punchier sound that is pleasing to most bassists.
Solid State Amplifiers: Solid-state amps use transistors for their preamp and power section. They require little or no maintenance, are lighter to transport and produce a very clean sound.
Hybrid Amps: These amps usually combine a solid-state power section with a tube preamp to provide the warmth and "musicality" of tubes with the durability and lightweight of solid-state. There are some manufacturers which combine both tubes and solid-state in the power amp itself. Hybrids have been very effective in bridging the gap between solid-state and tube amplifiers.