If you mean mountain biking, you'll only have to drive 10 min or so to find some really cool trails.

There is a gravel path around the campsite if I recall. I guess you could ride a bike but it wasn’t a very long trail. I walked it with my dog and took about 20 minutes.

The Spur Trail is nearby, mostly flat with lovely views. But it's not "from the park".

Not really. See previous answers. They are decent answers.

Not that I know of...

The Dinosaur Bikeway (3 miles long) is close but still 2.4 miles away next to the fire department Rancho Viejo Fire Station, La Cienega District (505) 473-1560 https://maps.app.goo.gl/eFENZee1vdobMg557. That highway mentioned in the first answer is what you'd have to deal with.

Not really. It's right off a pretty major road ( highway) so we found it not so bike friendly. You can tool around the park or in the adjacent neighborhood but that's not so far.