we have a misunderstanding... bluetooth seems to need RTS/CTS control

I think this is your misunderstanding:
Bluetooth, per se has nothing to do with RTS/CTS.
RTS/CTS is just one particular RS232 flow-control mechanism; Bluetooth is not limited to RS232 alone, and RS232 is not limited to CTS/RTS alone.

If your particular module is limited to RS232 with CTS/RTS, then that is a limitation of your module, and not a restriction of either Bluetooth or RS232. If this is not suitable to your application, then you need to get a different module (or maybe understand better how your module can be reconfigured).

If you are sure that you won't have flow-control problems, you could simply ensure that the module's CTS input is always asserted; eg, by linking it to the module's RTS output.
(Remember that old MS-DOS serial IO used to require this!?)