A method and system for controlling access to a bus for transferring data in the form of multibyte data streams. Data transfer agents are coupled to and request access to the bus to transfer data thereon. The system for controlling access to the bus comprises a bus arbiter responsive to the access requests of the data transfer agents, granting access to the bus to one data transfer agent at a time. A data length counter accumulates, during the grant of access, signals indicating the length of the data transferred between the bus and the data transfer agent. The data length counter indicates completion of the transfer of a predetermined length of data, and bus arbiter logic responds to the data length counter indicating the transfer completion, causing the bus arbiter to terminate the grant of access to the data transfer agent. The control of access to the bus is thus based on the precise measurement of the length of the transferred data, rather than on timers.