It looks really different from my ponytail palm but I couldn't even guess what else it could be.
Their are a couple of concerns with plants that you are denying enough soil to (bonsai).
First is they need to be feed frequently. There are special bonsai fertilizers or you can use osmocote (a slow release fertilizer you can get at most hardware stores), or even just watering with houseplant fertilizer will do.
Next is you need to repot every year or two, trimming the roots when you do. This promotes new fine root development which is neccessary for plant health.
Most Bonsai are grown outdoors, this is because most plants that are chosen for bonsai need direct sun. Ponytail palm will grow outside in Southern California but if you are north you will need to bring it in in winter. I have mine growing in dappled shade but morning sun would probably be better.
The less soil the more often you are going to have water.
I sometimes plant my "bonsai" in slightly larger pots, ups your success rate and the amount of watering.
Bonsai in shallow pots can need to be watered daily.
There's tons of information on growing bonsai out there.
You might want to check into proper soil mixes too.
The ponytail palm was a good choice.

Thanks! I'll be buying some books to start out! =)