I found it rather frustrating that one can have either original firmware or MicroPython installed on Bit device.
So I have created custom firmware (based on original one) that can easily switch to MicroPython and back (without lengthy installing and erasing game data, etc).
Here is the guide so anybody can create such firmware (and tinker with it):
MicroPython is started by running Snake game (I was lazy to add another “game” so I have piggy-backed on existing one). It will appear to do nothing, but in this state it can be connected on CircuitBlocks page.
To return to original firmware, just reboot the device (or disconnect USB cable).