Hi. I am not exactly your what you are trying to say. That's probably the reason that is keeping others responding to your question. But if I may, I would say something like:
Could you please send me the expense details for your reimbursement.
Cloud you please send me your bank details for your expense payment
I read this as asking me for details of my bank account, so that a payment can be sent direct to my bank. It sounds a bit odd to me, as in my experience such one-time payments are not handled in this way, but anyway, assuming that's cor