I just returned from a bike ride around the neighborhood -- a ride for cross training.  I use a mountain bike, because previously I rode trails quite a bit, but now I use it on the roads mostly.  I found, though, that these days they sell tires that work for both off-road and on-road -- they are knobbies with a slick strip down the center.  

It probably doesn't matter much whether you're using a road bike or a mountain bike for cross training, but a road bike should go faster.  The disadvantage of that, of course, is that you'll get hurt more if you have a spill.  I'm happy to stay with my slower mountain bike: for me it's about time, not distance.

Reading about riding recently, I came across an article with three good hints that I'll pass along.  I tried all of these on my ride today, and they really seemed helpful.  So here they are:
  1. Cadence.  Aim for a cadence of about 120.  This means that you complete a full cycle every second, corresponding with 120 "steps" per minute.  I found that holding to this cadence by adjusting my gears actually made the ride seem a lot easier than when I would allow the cadence to vary.  In practice, I could not hold that cadence on the very steep parts, but I set that as my goal and stayed with it as much as possible.
  2. Use the upstroke.  I use toeclips (old-fashioned, maybe, but better than nothing!)  I imagine cleats will work just as well in allowing you to pull up as well as push down on the pedals.  The benefit of this is that you get to use more muscles in the leg, reducing the strain on your quads.  It works especially well, I found, on the uphill stretches.  It doesn't exactly prevent the burn in the quads for me, but it definitely makes it less intimidating.
  3. Freewheel.  Keep pedaling on the downhill sections, rather than cruising with your legs in a fixed position.  You'll be freewheeling most of the time, so your legs are still resting, but they will dispose of the built-up toxins more readily than if they were not moving.  I found that my legs were a lot less stiff than usual when I started walking at the end of my ride.  
By the way, your stretching will feel different after a bike ride than a run, because you used different muscles.  I notice it mostly in the Achilles stretch: my Achilles tendon is not as flexible as it is after a run.  Be careful to avoid a tear here.

Happy cross training!