Does your gym have instructors or counselors who can help you to formulate a program? I've gotten about 5 programs over the year I've belonged to my gym, and it's really helpful to have a plan handed to me!
I can do a full body routine in about 30-40 minutes, and twice per week is enough for me to notice improvement. It's amazing what strength training can do for you, I highly recommend it unless you have some compelling reason to save all your energy for the bike!