Good beginner workouts on stationary bike
How long do you have?  How strong is your motivation?  How good are the bikes?

Unfortunately, most exercise bikes have a very poor "simulated feel", and a real cyclist tires of them pretty quickly.  This is especially true of the old friction bikes and many of the wind and magnetic trainers.  A few (Expresso bikes, and some of the newer Le Monde bikes that I've tried) do have a halfway passable "feel", though, since they have a modicum of momentum (which is the main thing missing in the others).

You can use the bike for several things -- short bursts, to raise your HR and short-term aerobic capacity, long sessions (at LEAST 30 minutes, preferably longer) to tax your glucagon storage just a hair and build endurance, and brief "climbs" to strengthen your muscles.

But, given access to a reasonably well-equipped gym, you probably should throw in some strength training as well, with leg presses, extensions, and curls.  And, believe it or not, simply being conscious to doing more squats through the day (eg, when reaching down to open a file drawer) can produce significant improvement.

And you really need longer sessions -- at least two hours at a crack -- to build your long-term endurance.  These are probably best done on a real bike, though, if at all possible.

I'm not convinced cadence is that important, but as a rough guide I'd say about 110 minus 65% of your age should be the upper limit, and 75% of that number would be the lower limit.  (Unfortunately, many exercise bikes only work smoothly at high cadence.)  My general rule for cadence lower limit is to never pedal slower than you're breathing, and that covers virtually all situations other than a brief climb.

Heart rate is also a guide, but there is much individual variation in rate, so it's hard to give numbers.