It comes down to a matter of resources. B doesn't have the emotional resources to deal with the loss of T and be fully present for you. You may not always have adequate resources to deal with B's turmoil and neglect. Believe me, I know what that feels like.
I have to agree with Kevin that it probably comes down to time. There is little that can be done to hurry the process. In my situation, E is very logical, makes rational decisions, completely understands his personal situation. However, he is often chagrined to find that understanding the issues does not make his turbulent emotions evaporate or enable him to always enjoy our relationship. The truth of the matter is, if I were not already on scene, I doubt E would choose to date anyone for some time yet. Might be the case with B too.
So you're right, it kind of comes down to patience, and putting in the work. And Kevin is right, self-care is important too.