"toe-touches" are very hard on a dysfunctional back, and will actually push a bulged disc out farther. Since you know being in lumbar flexion on the bike is putting pressure on the nerves coming off your spinal cord, going into lumbar flexion as an exercise before addressing the nerve compression doesn't sound like a groovy idea to me.

Did your chiro suggest any lumbar extension exercises? Or at least some NON-weightbearing lumbar flexion exercises?

Do you have a primary care physician who can get you into some medical care for your back?