Octal Bus Transceiver Not Working
The way that part works is as a bidirectional driver.  There is an active low output enable. If that is high,  A and B are effectively disconnected from one another. If that pin is low the behavior depends on the direction pin. If direction is high then A is re input and B is the output. If directing is low then B is the input and A is three output. 

If you want more feedback,  post a schematic of your circuit with the part in context. 

When the input is floating and output is enabled,  behavior is undefined. Really it's based on parasitic capacitance.  The delay you describe could be the hysteresis built into the part as the inputs are technically Schmidt-triggered.