BS here. I agree: intimacy is more than sex. I assume you are aware of that and aren't just interested in sex otherwise I think you've missed the boat here.
But assuming you do, it was a real revelation for my WH and I to take the Love Languages assessment. You can take it free online- just search love languages by chapman. Just because you like something doesn't mean your spouse likes the same thing! For example, i like it when my husband puts away the laundry. It makes me feel that he is trying to make my day easier. It makes me feel thought of and important to him for him to take initiate in his own to do something for me. My Husband doesn't enjoy doing laundry but hr does it for me. On the flip side, my husband doesn't get affected by the same type of thing--me having his lunch packed for work doesn't make him feel loved, he doesn't register it like I do.
Find out what your BS needs to feel loved and do it CONSISTENTLY, throughout the day even if you feel no progress.
It is very difficult for your BS to want to acknowledge what you are doing right because their first thought is "he's only doing x because he feels bad about...". The natural inclination is to pull away because of the pain and insecurities they are now living with. Your job is to prove that you really are sincere and work to regain the foundation that trust is built on before you can rebuild trust.
Little things throughout the day go a long way. When was the last time you bothered to write her a love letter, send her a simple "thinking of you" text during the day, have the coffee or supper made, hold her hand or rub her shoulders(if she comfortable and with no expectation or anticipation of sexual overtures). These are the daily little things to do for her each and every day--even if you aren't feeling it. This is the way to rediscovering intimacy after trauma like you have inflicted.
