Is order of bits in byte really not of concern?
Bytes are transferred from memory to disk using an I/O protocol (e.g. SCSI) that specifies the bit order of transmission in the case of a serial protocol, or for parallel protocols specifies which pin upon which each bit in a byte should be transmitted. For bytes moved from memory over the network, the network link level protocol (e.g. Ethernet) specifies the bit order.  In either instance, an application programmer need not concern herself with the details; the operating system in concert with disk or network controllers will maintain the correct bit order end-to-end so that the correct values are transmitted/received or store/retrieved.

N.B.: byte order is another matter altogether.