Albuquerque

If you have a military affiliation, the Fam Camp at Kirkland AFB might be a suitable choice.

A problem with the Rail Runner is the extremely limited schedule. For example, from Bernalillo to Albuquerque, these are the only weekday departures that will allow you a return to Bernalillo (the latest you can leave downtown Albuquerque for Bernalillo is 6:48 p.m.):

6:43 a.m.
8:18 a.m.
2:07 p.m.
5:20 p.m.

Several years ago I stayed at Palisades RV Park and used the bus to go downtown. Straight shot, no transfers. Pretty typical bus-riding experience, which is to say not great.

BUT the RV park was a pretty skanky place. We stayed in one of the spaces up in the front, which was nearer to road noise but away from most of the residents. So I don't recommend it, but if you need to be able to take the bus, at least it's possible.

My brother just stayed at the Bernalillo KOA. He said it was an oasis in the desert. 1 mile walk/bicycle/ride to the train station which will take you to downtown ABQ or into Santa Fe.

http://koa.com/campgrounds/albuquerque-north/

Cliff

Based on the OP's requirements, the KOA is the only option. If you are willing to take the rail runner instead of a bus, the other options may be better. While the KOA is pretty nice it is in a fairly high crime area of the city.

We gave this place Route 66 TV Resort a whirl in March and loved it.

Oops I missed the part about bus access.

We have stayed at the Abq KOA that is east of downtown--near our friends and easy access to other interesting areas.

Use the Rail Runner instead of the bus. Stay at the Isleta Puebleo RV park at exit 215 on I-25 and ride the rail runner into town. The rail runner also runs through Bernalillo if you stay there.

We liked the Coronado Campground run by the Town of Bernalillo just north of Albuquerque. Here's a link to a post I did about the campground....

Overlooking the Rio Grande: Coronado Campground