The Analytic Account is absolutely the right way to go!
Two requirements:
1) There must be at least one Sales Order in the system for the Customer. It can either have a Customer specific analytic account on it, or a Sales Order specific account set on it.
2) The product on the Vendor Bill needs to be set-up as "CAN BE EXPENSED".
The Analytic Account for the Customer (or for a specific Sales Order) is then selected on each Vendor Bill line that is to be reinvoiced.
Once the Vendor Bill is validated, Odoo will add a line to the relevant Sales Order show it will show up in the To Be Invoiced menu in the Sales app.
If only part of the line is to be reinvoiced, the line is split into two halves - the analytic account is set just on the half to be reinvoiced.