We currently run the SPI bus on the Bitsy Plus at about 900kbps to talk to the touch panel controller. Linux kernel version 2.4.19-rmk7 includes a general purpose SPI SA1110 driver that might work for your needs, or you can modify the touch panel SPI driver. If you create a driver that uses both the touch panel controller and your external device, disable the touch panel interrupt during external SPI communications to prevent interference with your device communications.
The Bitsy Plus system controller includes a 2:1 multiplexer that directs the SFRM (device select) signal from the SA1111 to either the touch panel or the external SPI device. Bit 0x02 of the Supplemental Controls Register(SUPPC at 0x10000014) routes it to SFRM1(onboard touch panel controller), bit 0x04 routes it to the external SFRM2 signal. (There's a protection circuit that prevents both of them from being enabled.)
Take a look at the touch panel driver and the Intel SA-1111 reference manual for further details about how to use the SPI bus.