Yeah I was able to catch a bus from Valencia to Teruel and then there is a bus (shuttle really) that leaves daily from Teruel and can take you to Albarracin. I don't think it runs on Saturdays. If I remember correctly it leaves Teruel at 3:30 but you might want to check that. There is a website for the Teruel station that will tell you the details. That being said, a trip to Albarracin without a car can be a bit of a struggle at times. The town and camping area are about 4.5km away from the bouldering area, so if you are planning on walking to and from the boulders every day be prepared for a nice uphill warmup.