Looking at General Handbook 24.3.4.2, this sounds much like the system for Young Teaching Missionaries - the church will set up a sub-account in the Ward Missionary account at the appropriate time. I'd image that payments can be made the same way.
Payment can be done via the Donation website. Other than having the bank send a check to the bishop's address (and putting the burden of filling out a donation slip on the bishop or clerk), I don't know as any direct payment is possible.
I'd advise against pre-paying for the mission as things can change and refunds are not allowed.
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