Sorry to hear about your wrist!
When you say long cast- how long? past the elbow? I can't imagine how you would ride if your elbow was immobilized.....
A fellow PT fractured her wrist while iceskating last year- she found she could take her bike out on flat roads but only after about 4 weeks. The problem earlier was her arm would swell and make the cast unbearably tight and painful. Not worth it in her opinion.
You might be better off doing an activity where you arm is not hanging down, a treadmill or elliptical where you could rest your arm at or above waist level for short periods
Good Luck