This is advanced stuff. Nice.
While this can be available on mobile phones according to the JSR-118 and JSR-82 specifications, I suspect not many handset manufacturers have actually implemented it.
Symbian provided a TCK-compliant reference implementation for Java BlueTooth Push to its licensees but testing it is a nightmare and I don't know whether either Nokia, Motorola or Sony-Ericsson actually included the funtionality in a phone.
My best guess of Symbian phones to try this on: Nokia N95, Sony-Ericsson P990 or W960, Motorola Z8. I would also advise trying on as recent a Bluetooth-enabled non Symbian Sony-Ericsson phone as you can find.
If you find a handset specification that actually says it supports J2ME BT Push, you then need to check whether that is supposed to work using RFComm, L2CAP or both. I don't know what your car kit uses.
As far as writing Java code to use Bt push, you can start by reading the example code in the 2 JSRs and the J2ME SDK from Sun Ltd.