Control over bus arbitration within a data processing system between a plurality of bus devices (101, 102) coupled by a bus (103) is performed in a user programmable manner by implementing logic circuitry that is responsive to a user programmable bit within a register (203) so that when the bit is asserted, the bus device (102) is able to maintain control over access to the external bus (103). Such a technique is useful for permitting a processor (201) to maintain mastership of an external bus (103) with respect to a direct memory access device (101) also coupled to the bus (103).