I may have a few ideas for you if you're interested. Since I haven't read your story I'm just going to make a few blind suggestions from what you posted on the forum.
1) Sesshomaru needs to go on a business trip and he takes Kagome cause she is his secretary and will help him during the meeting. You can add a sexual tension scene or two during this trip like when they are stuck in a vehicle together and then when they are in the elevator. Then after the meeting he takes her home and is nice enough to walk her to her door and enter another intimate scene. (If this is too vague feel free to ask for more help)
2) Kagome finds out Sesshomaru is sick and has no one to look after him cause he thinks he can take care of himself, but she insists on going to his place and looking after him. You can also enter an intimate moment in here.
3) Perhaps Sesshomaru gets jealous when he sees Kagome laughing and being friendly with his brother and is none to subtle about it.
4) How about an office party at Sesshomaru's company for whatever reason and you can add that they danced or actually got to talk to each other other than work related topics.
5) Kagome (or Sesshomaru) has a family member who had an accident and Sesshomaru insisted to be there for her.
6) Kagome could be having an ex boyfriend harassing her and Sesshomaru is there to stand up for her. Or you can say Sesshomaru has an ex trying to get back together with him and Kagome is somehow convinced to pretend to be his girlfriend to get the other woman to leave him alone.
7) Sesshomaru convinces her to go have coffee with him.
I hope these ideas will help you
If you need more help I'd be glad to think up more for you or help you expand on an idea.