First thing I thought about - though if you're looking to do this with a Raspberry Pi as a purely educational tool, it may be easier just to create the pure-python tool as a layer on top of linux.
Depends on what you're trying to do; both are useful. Booting to Python under Linux gives you an exploratory environment with access to operating system services, but not necessarily one that lets you poke directly at hardware, unless you put Python in the kernel. (And even then, the kernel and drivers are doing things behind your back.) BITS gives you direct access to hardware and firmware, and it's intentionally single-tasking, running only what you tell it to.
So if you want a comfortable Python environment with more services and the ability to use the full power of Linux, you would want to boot to Linux and run Python (possibly with some extra modules); if you want raw access to hardware and firmware, but without any OS (with all the advantages and disadvantages that implies), you want BITS.
