Some basic bouncing

F=ma
a=F/m

I hit the ground with a velocity on the y axis of 50 m/s. Accelerating simply with gravity (9.81)
Newtons third law, any force has an equal opposing force. So I hit the ground going 50m/s, for some basic bouncing (very basic) shouldn't I be able to take the current velocity, acceleration and somehow determine the new force to push upward.

Yes.
For perfectly elastic collisions (read as fiction/fantasy), the new velocity is 50 m/s.

Also, before hitting the ground, your sign should be negative if up is positive for your axis. -50 m/s before, and +50 m/s after.

Again, if up is positive (I believe for your application) gravity acceleration is always constant at -9.81 m/s².

I think you will like this java applet at this site. I didn't check it out completely, but it looks like you can adjust elasticity and gravity, etc.
http://www.myphysicslab.com/collision.html

Edit: Their gravity is positive instead of negative at the website