Greetings. I live a bit southwest of Paso on Morro Bay. I've never actually been to the GWBR (paid admission) but I've been ridden in Paso on that weekend several times. Be prepared for some heat. It's usually in the 90s or even 100 degrees.
There are four ways to get to Paso from SLO. The most direct way is over the Cuesta Grade. This is the path that Highway 101 takes. From downtown SLO, take Monterey Street north until it gets on 101. Ride on the shoulder of 101 until you see a sign for Stagecoach Road. I think they've built a tunnel under the highway now, but the last time I rode this they were still working on it so I'm not sure. Stagecoach road is a dirt road that parallels 101 to the top of the Grade. When you get to the top you follow a paved road that goes down the other side, next to the highway. At the bottom of that there's a trail on the left that takes you back to the shoulder of 101, this time the southbound lanes. You ride on that for 1/4 mile or so until there's a place to cross the highway. When you get across to the northbound lanes you ride on the shoulder to the Santa Margarita exit. Take that and follow El Camino Real all the way through Atascadero to the end. When I've done this route I've only been going to Templeton, so I rode back on the highway shoulder until the Templeton exit, where I've gotten off and headed back to the coast over Santa Rita Road. To get to Paso I suggest you do a Google Map search.
The other ways to get to Paso involve going out to the coast from SLO, north a bit, then over the mountains. One way is to ride on Highway 1 to Morro Bay, then turn right onto Highway 41, which takes you over the mountains to Atascadero. However, I would NOT recommend this. 41 is a busy, twisty little road with absolutely no shoulder, steep walls one side and a dropoff on the other. I think people who ride it have a death wish!
The more normal way to go is to ride up Highway 1 almost to Cambria, turn right on Highway 46, and take that over the mountains. It has a nice shoulder all the way and takes you directly to south Paso. When you get to the end at Highway 101 you can take a frontage road on either side of the Highway. I'd turn left just before 101. You should be able to ride right to the fairgrounds, which are on the west side of the highway. That will be a pretty long, tough ride. It's about 55 miles, and the climb over Highway 46 is long - not overly steep, but it's a long climb.
Another way that I like, would be to ride to Cayucos on Highway 1, then turn east on Old Creek Road. After you pass the reservoir, down at the bottom of the hill there's a turn to the right on Santa Rita Creek Road. (Google calls is Sant Rita Creek Road; everyone around here calls it Santa Rita Road. I don't know what the sign says, but it's the only road to the right after you get to the bottom of the hill by the reservoir.) Santa Rita Road becomes a dirt road that goes all the way over the mountains and drops you into Templeton on the other side. This is best with a mountain bike, but I've ridden it with my touring bike several times. It's a quiet, beautiful ride through the countryside.
Once you get to the GWBR, there are lots of options for good rides. I don't ride in Paso that much, since I have to drive half an hour to get there, but some of the routes I like are the Peachy Canyon loop, north to Santa Miguel (on River Road) and back, out 46 to Estrella River Road, then loop northwest to River Road and back to Paso.
Check out the www.slobc.org
website. There are lots of route descriptions there.