Here are some of the choices:
You can use most solid state amps without a cab.
You can use a preamp.
You can use a cab SIM or IR loader.
Some small tube amps like the Ampeg PF20t, Ampeg PF50T, and Ashdown LB30 2.N have a built in dummy load and can be run without a cab.
You can use a load box and DI with tube amps that do not have a built in dummy load. Caution is advised, as you need to make sure to select a load box that can dissipate the amount of power the amp will make. A load box that can safely handle a big tube amp will be expensive.
The main advantage of using an existing head is you don't have to spend any money.
If I were going to do an ampless rig, I could use my Empress ParaEQ and a regular DI. This would allow me to have some control over how my bass sounds in the IEM mix. I might even consider adding a compressor pedal in the signal path. Alternately I could get some sort of Preamp DI like the Mesa Subway, Tech 21 Q/Strip, or MXR M81.
As you see that are lot's of different ways to approach this.