To respond to your queries:
1)Bus Service: It does NOT regularly service all the way out to Rum Point. The closest regular stop is Chisholm's mini-mart about 5 miles away. If you catch the bus from town, they MAY take you all the way out to Rum Point with some di$cu$$ion. A rental car(s) are highly advisable.
2)Sting Ray City: Crowds vary and are most affected by the number of cruise ship visitors. Staying at Rum Point you have the option of taking an afternoon or even a weekend tour with RedSail that will pretty much may result in a visit devoid of cruise tourists (since they will have long headed back to their tender lines). Also, for any planned trips to Seven Mile Beach, George Town or other "tourist" spots, refer to the Cayman Port Ship Schedule Calendar to plan visits on lighter volume days.