BJT Constant current LED driver
I'd be using 5V and a MOSFET here to limit the current required from the GPIO and coupling it in a typical current limiter as shown below.

R1 and Vbe or Q1 roughly set the current limit. If you need it more accurate than that you either need a pot in there or a more active circuit.







simulate this circuit &ndash; Schematic created using CircuitLab

The gate threshold of the MOSFET needs to be under or close to 1V. Power lost to the MOSFET is about 300mW and R1 is 215mW.