With a Pedal Hop
The pedal hop is a nice controled way of climbing on bars, wall edges and corners where the front wheel will need to be higher than the rear wheel. This is not a bunny hop. Rather than brute force, it offers much more control.
Counting the pedal strokes...
° Start about one full crank turn from the obstacle on your good pedal (Fred is right-foot).
1° Pedal slowly and use the bad foot (left pedal) to lift the front wheel towards the obstacle. 2° Accelerate with a kick in the good foot pedal (right-foot) while extending the legs like for an impulsion upward. 3° The impulsion sends you off the ground, carry on pulling on the bars and fold up the knees to let the bike take off.
See the move in a video

More tips?
The same way the bunny hop could be seen as a backhop launched while riding along, climbing with a pedal hop is like launching a pedal hop while rolling along. It is important to get your distance marks, so that you know when to start lifting the front wheel with the goofy pedal, following up with the good-foot pedal kick and extension.
This move offers much more control than a bunny hop. Rather than just a kick in the pedal, from a static position, you are already doing some smooth crank turns to move forward the obstacle when the pedal kick comes in (acceleration).

The next move is to hop from one beam to another using the pedal hop technique. This is just like giving a good pedal stroke to jump over a gap, very spectacular and classy in demos.