My LPG conversion needs to warm for about a mile or so before switching to gas, so I'd guess a factory bi-fuel would be the same.
The reason for this is because the LPG has to be vapourised before it gets via the injectors and into the combustion chamber. This vaporisation is achieved by warming the LPG as it reaches the engine bay.
This is done by passing the LPG through a regulator that is heated by means of a water jacket. The hot water to heat this jacket is provided by the engine's cooling system - which only gets hot enough to do the job once the engine has reached operating temperature and the thermostat is fully open.
If the temperature isn't high enough then the vaporisation doesn't happen efficiently enough and thus trying to run the engine on LPG (Liquid Petroleum Gas) that is more L than P means it will do a pretty good impersonation of a three-legged dog!
I do know that it is possible to start and run an engine on LPG from cold, and one or two posters on here do have older LPG-only cars. Classicswede will be able to explain more fully, but I'm not sure it's possible on more modern engines with sequential injection LPG systems.
As far as I'm aware though, modern sequential injection LPG systems do need the engine to be fully warmed up before they'll run on gas.
Useful link:
http://www.autogas.co.uk/converting.htm
You might be able to get an LPG expert to twiddle things a bit, and I guess anything you can do warm the engine up quicker will help.
One cheap and easy thing you could fit is a new thermostat. The other would be to change the LPG filter. It won't do any harm, and might indeed help a bit.
Cheers
Jack