You can ride your bike around the campground loops and on the desert trails that border the campground. Or, ride on the road, which is narrow with no shoulder.
Mtn bike trails leave right from the campground. We enjoyed riding them, especially since we didn’t have to pack up our bikes to find trails. No paved trails that I recall.
Yes, there are 50 miles of bikable trails accessible from the campground. All trails in Tucson Mountain Park are multi-use (hiking, biking, equestrian). A popular intermediate level bike trail nearby is the Ironwood loop. TMP trails map:
https://content.civicplus.com/api/assets/7855a351-bf2f-4a1b-9ac1-edb047a72e2b?scope=all
Yes, check out this website for details since riding your bile on the roads is not safe.
https://www.gaiagps.com/hike/poi/united-states/arizona/tucson-mountain-park/gilbert-ray-campground/