Nope, most lightweight rifles really do not shoot well of bipods. Bipods work well on heavy barreled rifles with free floating stocks. If you want a stutzen or other lightweight rifle you will have to learn to shoot well by holding the forend properly. You can always support your hand, and with a bit of practice you can get very proficient. With my combination gun, or my Rigby, neither of which can take a bipod, I have taken longer shots using a backpack, a rolled up coat, or more usually my binoculars on their side.
Or you just sit Loosing bipods and other shooting aids takes a leap of faith, and plenty of practice, or reminding yourself of childhood days with an air rifle.