Bullseye shooting has been compared to golf - fun but can be frustrating. If you don't have a desire to improve, it's no good. But if you do it, you will be a better shooter. I belive it's the only shooting sport where there has never been a perfect score recorded (2700 of 2700 possible).
Cycling doesn't bother the sight noticably. Remember, that for a Bullseye match, zero is the X-ring (0.67 in. @ 25 yds and 1.70 in. @ 50 yds.) and lots of things may change your zero on any given day. Change in light, slight change in grip, position of trigger finger, caffiene, etc. So, you are always aware of where your group is and you may change the zero at any time. Right now, the Ultradot brand of scopes is the sweet spot for durability, performance and cost. The 1 inch Ultradot on my gun is only about $130, although I've got 30 mm Matchdots on some of my other guns that are in the $210-$220 range with more bells and whistles. Those aren't necessary, the 1 inch Ultradot works just fine. What is probably best, and we're starting to see now, are small Aimpoints. Great sights, but expensive and there is no mass market mount available for a 1911, you have to get one built. That runs one of those out close to $1000. Remember what I said about Bullseye shooters being frugal?
Most Bullseye shooters and 'smiths mount the sight on the slide. The reason is that the barrel in a 1911 locks into the slide and so the sight is more closely aligned to the barrel than it would be when mounted to the frame. This negates any slide to frame misalignment, but you are still at the mercy of the consistency of barrel lockup. With a tight gun, a frame mount works and some high end gunsmiths prefer them. If you buy a Les Baer Premier II, e.g.; a frame mount is an option. Now, you might ask why we don't use a holo sight like the run and gunners? That's because a holo doesn't do well in the rain or really bright sunlight conditions. Matchdots come with extra tube extensions for shade and a polarizing filter so that you can eliminate lens flare and get contrast for the dot. This is one of the problems with the Aimpoint as well, you need to get a tube extension fabricated for it to get over some of these issues.
Sorry if this was long an is a bit of a threadjack. But, you all seemed interested.