My first thought is that this sounds like a personality thing. What we, as humans may see as bullying, may merely be a timid younger cat that naturally sees the other cat as more alpha. I have a cat that I rescued from outside when he was six-months-old. He was semi-feral at the time. He is a HUGE tomcat. Of my current five cats, he is the most timid, and naturally defers to all the other cats and my dog. Even my newest rescue, a tiny five found tortie intimidates him.
If you feel that you're not able to give the other cat as much affection as he or she wants, I suggest trying to make time spent with you super pleasant for both of them. Get some treats and be sure to feed several to the dominant cat first to keep him or her occupied. Give the other one some treats as well. Pet them and talk to them.
For the most part, remember that the arrangement these two cats have may just be what is natural for them. It will definitely evolve over time. I've noticed that about my cats. But it changes slowly over months and years. Make your home a positive experience, and your interactions with both cats positive.
Most of all, feel flattered that one cat is very demonstrative of his or her affection for you. It's a compliment for sure. Hang in there.