You can do self-resistance bicep curls and isometric bicep curl holds.
Curl your fist on your right hand and resist it by pushing down on your fist with your left hand.
You can do a version of a chin up/pull up with a towel draped over the top of a door.
You can also try "virtual resistance training" where you visualize you're lifting a 100 lb dumbbell (or bigger!) and go through the motion of the bicep curl, but really concentrate and contract the muscle.
One of my favorites is the one arm chin done as a DVR (dynamic visualized resistance).
Here's a demo: http://www.transformetrics.com/content/one-armed-chin-0
As you bring the arm down, you are contracting the muscle as hard as you can. It really works