It looks like you already have the makings for some brick workouts with your gym setup. Once or twice a week follow up that 1 hour on the stationary bike with a mile or two of running. If you haven't done a tri, you'll never be able to appreciate the uniquely dead feeling in your legs as you come off the bike and start the run. Take short quick strides, make your foot-strike directly below your body and keep you knees low so you don't rely on your quads for running. They're dead meat from the bike anyway so don't expect them to be much use for the rest of the 5K run.

Getting the maximum performance out of your body in a tri is very much about good efficient, economical technique in each of the 3 legs. The quality of your technique will determine the energy you use to move yourself forward, and you want as much left for the run as possible. Your technique will also determine which muscles you use for each sport. This is especially important when transitioning from the bike to the run if you are a long striding, knee lifting runner. You ideally want to use different muscle groups when biking and running. I would highly recommend getting your hands on a book titled, "The Triathlete's Guide to Run Training", by Ken Mierke.
Web site, http://www.Fitness-Concepts.com/ . It will give you the full biomechanical understanding of how to adjust and optimize your running technique, as well as how to improve your bike technique so that you will run faster. This book is a lot more than just running technique. It has almost become my tri coach.

Your chosen triathlon has a 300 yd swim, which means the few weeks you have to train when you get back will be just fine. Here too technique is important. If you have a sloppy swim stroke you will exit the water winded and may have to take it easy for the first few miles on the bike. You probably already have all the upper body strength and cardio conditioning you need, so your limited time may be best spent improving your technique. I recommend the book "Total Immersion, the Revolutionary Way to Swim Better, Faster, and Easier", plus the companion DVD "Freestyle Made Easy", both by Terry Laughlin.
Web site, http://www.totalimmersion.net/index.html . If you follow Terry's methods and do the drills he shows on the DVD exclusively for a couple weeks, the swim portion of your tri will be a cakewalk.

I know I'm putting a lot of emphasis on technique, but that doesn't mean you don't have to put in the miles. You really want to be fit, but you also don't want to waste that fitness on inefficient and counterproductive movements. So, again I highly recommend the above books and DVD. And good luck in your tri this coming May.