If you purchased 2 months ago you should have version 2.1u. Especially since you have firmware 2.0.3 — only hardware 2.x runs firmware 2.x.x, the earlier 1.4 cannot run firmware 2.x.x. If you are not sure, you can open the enclosure and the version number is printed on the PCB.
Anyways, I assume you have 2.1u. To enter bootloader, unplug USB, then press and hold B2 while plugging in USB, and release within 1-2 seconds. Note that the screen should remain off — if the screen lights up, it didn’t enter bootloader successfully and you should try again. On Mac you don’t need to install driver. The device manager should show a USBasp device. If it still doesn’t work, you might want to check if the USB connector is soldered correctly (i.e. no solder bridges etc.).