We flew with Ryanair in May/June. When you are checking in they put a tag on the pushchair and you have a choice of l through or taking it with you until boarding. All pushchairs were taken by the staff at the boarding gate, perhaps about 10 min before boarding began. We only had a cheapie pushchair though, and can't remember if anyone else had a bulky style. In the past I've taken the pushchair right to the door with them, I think it will vary from airport to airport. When they take it, ask them if you can have it back as soon as you land, otherwise you have to wait until it comes out with the luggage (or worse, have to start searching for the area where the prams/carseats are left)
I've gone with Ryanair and had no problems with bringing travel system right to plane steps (pushchiar plus car seat clipped on). Like previous poster said, they'll tag each piece when you check in. Some airports have luminous tags for "immediate delivery at planeside" for when you land so the baggage handlers will see it. On one occasion, only the buggy part was given at the steps when we landed and the car seat went in to the terminal with the rest of the luggage, but that was fine, I had the most important part!
bacon, I think the website means that you have to go to the baggage drop to get a checkin tag for the buggy - not that you necessarily have to leave it there. It has to have a tag whether or not you wheel it yourself.
Certainly in the past Ryanair have always allowed you to take the buggy to the plane steps, in fact I think this isn't up to them anyway, it's the baggage handlers who deal with it, and they're part of the airport afaik.
Do be aware though that the buggy is usually sent to the baggage claim conveyor belt when you get to your destination airport not left at the steps, so you might still have to carry your baby quite some way - a sling can be useful for this reason.
Maybe you could ring bristol airport though, as they will probably answer your question without charging you an arm and a leg.