I have not tried this, so it is just speculation. There are many claims online that a recumbent bike cannot be bunny hopped. However, lifting the front wheel should be possible while sitting on the bike, because lifting the front caster of an office chair is possible without touching the floor. Lean forward, then slam your torso back against the backrest – careful that you don’t tip over backward. Your legs may be lifted or the feet may rest on top of the “spider” at the bottom of the chair.
On a recumbent, a further boost comes from suddenly pedalling hard in low gear, which accelerates the rear wheel forward and under, rotating the front wheel up around the pivot of the rear wheel.
Lifting the rear wheel of a recumbent should be possible while seated, because popping your butt off the floor when sitting with straight legs is possible without using your leg muscles. Put your fists on the floor slightly behind and to the side of your hips. Bend your elbows, then suddenly straighten them, pushing explosively against the floor. Your butt and your fists lift a few inches. Keep your legs locked straight. Very strong people can do this with legs lifted (in boat pose: body in V-shape with only the butt and fists touching the floor).
Because lifting each wheel is possible and the movements do not directly oppose each other, a recumbent should be bunnyhoppable. Lift first the front and then the rear wheel.