Heres how I handle my asexual character Carissa Kuronas. Carissa is very uncomfortable around others (this has nothing to do with her sexuality) that are not Cameron Moriantes. With Cameron Carissa is generally relaxed, she loves Cameron she enjoys sitting on the couch with him and watching TV. She enjoys walking the streets hand in hand with him adoring the beautiful scenery. The couple have had "the talk" many times; Carissa hates having the talk, sometimes Cameron moves his hand a little closer, Carissa nearly cries when she sees the look on his face when she tells him to stop. She doesnt want him to leaave her, find someone better, find someone who will let him do as he desires; let him do what she cant.
Cameron loves Carissa. Carissa keeps Cameron grounded in reality, she keeps his head on straight. Sometimes Cameron gets carried away, Carissa will stop him, Cameron will apologize. Cameron would never leave Carissa, she means too much to him.
How would you write an asexual character? Or any other sexuality, whichever you wanna talk about.