The amount of time it takes is a bit variable. It depends where you are coming from. It also depends a bit how crowded it is at your bus stop and MK. (random moderate crowd day vs. major holiday) Major holidays mean slower pace. this may be TMI, but here goes:
Personally, we usually end up arriving about 9:15ish. Even the times we think we're early, the bus doesn't show. But often we are at our bus stop between 8:20-8:30am.
From CR, it's about a 15min walk to MK, with extra time for bag check.
From other resorts, it could be 20min for bus to show, plus 20min ride, plus another ten to walk from bus stop and through bag check. You generally don't hit the trifecta of all three parts being the max time. If you are at one of the big mods, allow extra time for the bus to loop your resort. (add ten min) If Rope drop is really important to you then add a safety margin. If you just want to be there about 8:40am RD, then 45min is a good general allowance from most resorts. (unless you are at CR or another MK area resort). Probably 8am is a decent time from most resorts.
As far as crowds, most days you don't have to be worried. It's pretty safe, and well regulated. It's not the number of folks that's a problem, it's that some of them can be rude in their quest to be 'first.' (and why I often avoid it.) They will get a little pushy and testy sometimes. Therea re a few spots in the park though where crowds are worse. the simple solution is to HOLD hands. After the fireworks, hold hands. Going by Splash Mtn, hold hands. Entering a theater, hold hands. Even adults!
Oh, and one more thing. There's always a small chance that there will be a problem reading one of your tickets. Likely all will be well, but it pays to know it can happen. That's another reason why we aren't die hard on RD.
