It doesn't sound like that stallion is trained well enough for you to go riding with (or on).
My neighbor had a stud at one point- and you'd never know he was a stud (exactly as it should be).
When loose in his pasture, he would prance and whinny sometimes (he LOVED it when the mares ran, he'd flirt with them all day, and turn on his "HEY! LOOK AT ME! I'M PRETTY! prance). But if you were standing next to him (with or without a halter, saddle, etc) he would do absolutely no more than ***** up his ears and look. If you were actually working, he'd rarely even do that. He was an absolute doll. We used to go riding together a lot, and never, ever had an incident.
But, as a general rule- I don't go out riding and being around studs unless I know them WELL and trust their behavior, and the person handling them. There's just too many problems that can happen- quickly- I don't want to risk myself getting killed, or injured- or my horse for that matter.
In your case, it sounds like it can quickly turn into a disaster.