All horses are stiffer to bend one way over the other. That's a fact.
Mine's hard to bend to the right (she's tight on her left side).
Rather than bending the horse around the inside leg by pulling the neck around with the reins (a crude aid used by those who don't know any better), do the horse a favor by helping him supple the side he's stiff on before getting on with more strenuous work.
I spend the first 15 minutes of my ride solely on warmup, and most of it on lateral exercises particularly small circles and serpentines at the walk. I always try to keep the stretching and warm up fairly even from side to side, but I always do bends/circles to the right a little more since that's where she needs more help.
Any time Calypso starts to show me difficulty in flexion to the right I stop what we are doing and go back into circles and serpentines to loosen her up further.