The ArduinoBit uses the ATMEGA32U4 chip. Similar to Arduino Leonardo or Arduino Micro
As was pointed out earlier, the CodeBit uses ATSAMD21 chip. Similar to Arduino Zero
Both are very different from each other in terms of capabilities. ATSAMD21 has tons more memory, but it is also more difficult to do things like softwareserial on ATSAMD21, which is relatively easy to do on ATMEGA32U4 based platform.
In theory you could burn the boot loader onto the ATSAMD21 chip on your CodeBit, but you might have compatibility issues. Also none of the ports would be clearly labeled on the board (e.g. Analog pins A1, A2, A3, versus Digital D5, D6), so it would be a challenge to interface your source code with external sensors/peripherals, you'd have to have some type of reference chart to translate the pin numbers.
It would be a neat idea but it would require a lot of effort to get it working.