I have recently been diagnosed with mild aortic and bicuspid valve regurgitation. I'm still waiting for more testing. Can I go back to exercising?

Valvar regurgitation. In general mild valvar regurgitation would not preclude exercise training. You should ask the question of the physicians who know you and diagnosed the valve problem(s) to get their input.
Possibly. The best person to answer your question is the Physician that diagnosed your issues. (S)he will be able to quantify the extent of your problem and provide you with guidelines as to stressful activities.