Traction control light comes on after about 15 mins at idle or driving .turn car off and restart light goes out but eventually comes back on car seems to drive ok with light on or off

Probably caused by the electronic throttle control . How many miles on the vehicle ? The gas pedal has position sensors that the PCM - engine computer uses to know how much to open the throttle plate .
Drive by Wire Function and diagnostics by Wells
What engine ?
The throttle actuator control (TAC) system is used to improve emissions, fuel economy, and driveability. The TAC system eliminates the mechanical link between the accelerator pedal and the throttle plate. The TAC system eliminates the need for a cruise control module and idle air control motor. The following is a list of TAC system components:
• The accelerator pedal assembly includes the following components:
- The accelerator pedal
- The accelerator pedal position (APP) sensor 1
- The APP sensor 2
• The throttle body assembly includes the following components:
- The throttle position (TP) sensor 1
- The TP sensor 2
- The throttle actuator motor
- The throttle plate
• The engine control module (ECM)

I'm sorry Roger but you are going to have to get it to someone with access to the plug in diagnostic unit for Beemers.
there seem to be several things going on but when it coughs up the diagnostic info you may go straight to it?

The reason for traction light to come up is due to high idle. Set the idling screw to proper amount and the check light may go off.

The stability system is software programmed into the ABS - antilock brake control module also the PCM - engine computer . service engine light DTC'S - diagnostic trouble codes stored . Your best bet , take it to a qualified repair shop or the dealer . You don't have the diagnostic equipment or knowledge to tackle this type of problem .

It is safe to drive. You need a scan tool to get a code out of it. Could be as simple as a wheel speed sensor going bad. All of these lights will work together normally. The traction control uses the ABS to gain traction, and the Brake Assist System is part of the stability control. Also uses the ABS.

Very common. Bad wheel speed sensor. Read this
http://ricksfreeautorepairadvice.com/abs-light-on-traction-control-off-gm-products/

ABS light on Traction Control Off GM products Ricks Free Auto Repair Advice

engine lights also report on the transmission problems
try having the fault codes read instead of fixing what probably ain't broke

the abs warning light also works with the electronic traction control, (or traction control,same system,different names) and when icy, stops the wheels from spinning,above about 15 mph.(the abs dont work under 5mph) so if im right regarding your question,your car is doing what its supposed to,stopping the driving wheels from spinning/locking up.the warning light comes on when one or the other is doing its job.(working).the trick is to drive so that the warning light doesnt come on..... boring.

pull the negative batery cabe off for 15 min and that shoul reset the comp if it comes back on you have a problem with your traction controll

sounds like a faulty wheel sensor.