What you're wanting to do is really not practical; you're coming at this from way too high a level and trying to imagine the system as if it were running an operating system from the word go.
When you get the STM32 it as empty shell; you need to program it to do what you need to do and the only [sensible] way to get register-level debugging is to use a JTAG interface.
If, and this is a big if, you get it working reliably, but just want to give some debug information back while it is running, you could write a load of routines within the code to send out debugging messages when it enters certain parts of the program - and send it out over Bluetooth - but this is nothing like what you're used to single stepping through your Java code with Eclipse. If you want to do that kind of thing, you are going to have to put a little connector on that allows you to connect your JTAG or two-wire debugger cable to the processor. Even then, when you do that, you will be completely resetting your program and not simply single stepping through from where it went wrong.
You could insert a monitor program within your program to send out register values, program status etc over Bluetooth, but you still have to write the inital code and the only way to do this with out a ridiculous amount of trail and error is via your JTAG or two-wire interface.