Gentlemen,
As a US Moto 6/5 owner, I am kinda on my own. So I have been addressing the carb problems on my Moto since I acquired it 5 years ago. Here are some things I've learned about starting and operation of the Rotax 5 valve. Open the fuel cock a few minutes before starting the bike. It seems the float bowl fills slowly and trying to crank on it before the bowl is full is going to prolong the starting process. Extending cranking on the engine is also a strain on the starter motor and spag clutch. If the bike becomes a very unreliable starter, check the ignition pick up unit near the sprag clutch or have a pro check it. Mine accumulated metal filings from a worn prag starter clutch that resulted in intermittent shorts, killing the signal to the CDI spark box under the seat.
Assuming your starting/running problem is in fact a carbonation problem--it starts with the enricher (choke) engaged but isn't drivable when cold--your issue is likely a lean mixture problem. At idle to 1/4 throttle, the pilot jet mixture screw located on the bottom of the carb controls the fuel mixture on the stock Mikuni BST40 carb. Assuming you don't have an air leak between the carb and cylinder head (spray the manifold and rubber hose area with WD 40 or some other light oil to see if it changes the engine speed to test for leaks), you may need to richen the pilot (idle) jet circuit by screwing the pilot jet needle out in 1/4 increments.
This screw is a pain to adjust particularly with the engine running because it is hard to tell how far you are turning it with a conventional screw driver. An easier solution is to purchase a fuel mixture thumb screw from Stenhouse racing in the US. See this link.
http://stenhouseracing.com/shop/index.php?main_page=product_info&cPath=5_4&products_id=1 There may be other such suppliers in the UK & Europe.
Regardless whether you use the stock screw or the Stenhouse type thumbscrew, with the engine off, turn the pilot jet screw clockwise until it bottoms out. Be gentle, don't try to tighten the screw once it bottoms in its seat. Keep track of how many revolutions you turned the screw and write that down as a reference point. Now, turn the screw back out counterclockwise 2 turns. That should get you in to the range where you can get the engine running and avoid stalling when pulling away. Don't expect the 650 Rotax to run smooth just off idle when cold, even when perfectly tuned. It requires some warm up. But at 10C or 50F degrees the engine shouldn't die when pulling away from a cold start. In fact, leave the enricher on for a 1/4 to 1/2 mile of running when the engine is cold. This will help richen up the mixture until the engine starts to warm up. Depending on conditions it may not fully warm up for 15 minutes or so.
You can fine tune the pilot (idle) mixture screw by getting the engine completely warmed up and experimenting with different settings to get the fastest idle and the best engine performance from idle to 1/4 throttle. If the bike surges in town when the engine is warm, the setting is probably too lean. Turn the screw counterclockwise in 1/4 turn increments to richen the mixture until the surging stops. If the engine feels boggy and doesn't like taking the throttle or seems to load up on fuel and gets poor fuel economy turn the screw in in 1/4 turn increments for sharper performance.
Be advised that the idle pilot/idle screw setting can be a bit different from 10C/50F degrees to 30C/86F degrees. That's why the thumbscrew pilot jet screws are so handy for fine tuning.
I hope this helps. If you want to discuss Moto 6/5 tuning in more depth, send me an e-mail at stradakat@gmail.com. I don't have all the answers but I've spent a good bit of time tuning on the Moto and can point you to some helpful resources.