Yes, Highway 12 is the best bet to get there from the 89.
As for camping, there are two campsites in the National Park itself. North Campground has 13 RV sites, and Sunset Campground has 80 RV sites available. You can review the information on the link I'm providing below.
Please note the following:
1. The campgrounds are closed in winter.
2. Sunset campground will be undergoing a major renovation from April 2014 through July of 2014, which result in intermittent closures of campsites and restrooms. There will also be a lot of construction noise, dust and traffic between 8am and 6pm.
There are quite a few private RV parks outside of the National Park which you can use if you can't get a reservation at one of the inside parks. An internet search will provide names of these parks.
Bryce Canyon Camping
2016 Ford F350 Turbo Diesel SRW 4x4
2017 Grand Design Reflection 297RSTS
2013 Ford F350 Turbo Diesel SRW 4x4 (Destroyed by fire - 8/29/16)
2014 Grand Design Reflection 337RLS (Destroyed by fire - 8/29/16)