The base resistor must be less than 4.7Kohm to ensure your BCP56 goes into saturation. I would suggest to use 2.2K
A resistor from base to GND does no harm, but does ensure that your BJT does turn off when signal goes low. 10K ohm should be ok.
A current limiting resistor is a MUST to safeguard the buzzer. With 5v supply you should use between 180ohm - 220ohm. (Check the calculations)
One question - why do you have two separate voltages - 3.3v and 5v. Why not drive everything with 3.3v ? If you do, then the limiting resistor should be reduced to 100 ohm
Do check the output drive capability of LCVMOS technology -- it needs to be able to source at least around 3-400uA for this circuit to work failsafe. This is because you have to use a worst case (lowest) hFE or Beta to ensure your circuit always works.
Lastly - I assume your buzzer buzzez simply when you pass current through it. Seeing you have written here detailed impedance/ current parameters, then do also publish the actual buzzer product page for our general knowledge.