I don't believe that there's a definitive answer to the 'correct' TPS setting, and neither do BWM because they quote a range and not a single value. The higher the voltage returned by the TPS for a given throttle opening the richer the mixture, so by adjusting it to reduce the voltage (measured with the throttle closed) you will make it run leaner and that adjustment will apply throughout the range of the TPS.
The ideal value will vary from bike to bike with different production tolerances and also with different modifications (air filter, Y, can etc). My advice is don't believe anyone who tells you a specific figure - just because it works on their bike doesn't mean it will work on yours. Spend some time adjusting it to different values and riding the bike - I've been changing mine once a week which gives me plenty of time (commuting - mixture of motorway, A, B roads and city traffic) to evaluate the results, and I reckon I'm close to getting it right.
Compared to your current setting of 0.375v it is by no means a foregone conclusion that reducing this will cause/increase surging - it certainly didn't in my case. But if you're happy with the way the bike runs now, as you seem to be, and unless you're a hopeless fiddler (like me
) maybe you should just leave it as it is?
As for setting the TPS with or without engine running, since all advice/instruction is to set it with the engine off why question it? With the engine running and the alternator 'pumping', the voltage in the system might increase enough to affect the reading, but I guess that as long as you're consistent in how you measure it that's the main thing. I'd still do it with engine off, though.
(that will be 121 mph then!)
