axi vs ahb
In AHB, there can be only one transaction per master (either a read or a write) at any time.
In which direction does your bridge operate? If you connect a single AHB master to an AHB-> AXI bridge (acting as a slave) and the AXI bridge is a master to an AXI slave, then there is not much scope for doing two transfers simultaneously (although you could buffer writes within the bridge, so that a read could be done while a buffered write is in progress).
In the other direction (more usual case) where you have an AXI master connecting to AXI->AHB bridge slave (and bridge is master to an AHB slave), then you can't really do two transfers at once. And you potentially have to worry about hazard checking so that reads and writes do not get re-ordered by the bridge.
Have you looked at the idea of dual-porting the slave (or master), so that reads and writes are on seperate AHB Channels?
**broken link removed**