Back in the 80's friend's and I used to ride our mountain bikes up the PCT like Paul did from the Mojave Forks Dam to DCHS. I think these days the rules for the PCT do not allowed mountain bikes or any " vehicles " in general. In the part of that route near the dam the PCT goes across a very steep hillside. People have died on bikes going over the side/ off the trail before. Another friend, a long time DCHS visitor was riding his horse with other friends with horses too in that steep area and one of the horses got spooked and it tumbled down the cliff to the bottom of the canyon. The rider luckily fell off the horse in time not to fall too. The horse was severely injured and had to be euthanized.
In recent years on my hikes in that area I have not seen any mountain bikes going up the PCT. The Power line Rd from Deep Creek Rd heading east goes up a mountain side for the first two miles, then after that its just hilly on over to the Freedom Trail parking spot. It is a route I have traveled many times in my truck over the years on my way to the springs and I have seen mountain bikers using that road.
I have before parked near the taller mountain out west of the Bowen Ranch, around where the power line road goes up it on its way westerly, then rode my mountain bike from there on the route to the Freedom Trail which would save you climbing up that steeper hill over by Deep Creek Road.
You could call a ranger station, one like Sky Forest up by Lake Arrowhead ( or the Discovery Center at Big Bear Lake ) to inquire about the rules for bikes on the PCT.
My brother was riding his mountain bike on the PCT on his way back from DCHS many years ago and he was going very fast down one of the steep parts of the trail near the Rainbow Bridge when he got some air over a bump and came down hard enough to break his handle bar sending him tumbling off of his bike. Luckily he did not break any bones or fall down the hill, but he did get a lot of significant abrasions on his back, arms and legs. I had an early 80's KHS mountain bike and my brother used to joke me, saying it was like the Harley Davidson of Mountain Bikes. It was pretty heavy but sturdy and I put a comfy " tractor seat " on it