I have a 99 Mazda Miata with Factory daytime running lights and an HID conversion kit I'm going through bulbs rather quickly due to turning the key from off to on the bulbs start to heat up then from on to start takes power away from the bulbs any ideas thank you

 

Unfortunately, the only way to do that would probably be to implement an override switch for the DRLs/HIDs. That way you could prevent all power going to the headlamps until the car was totally on and not cycling power. But it's effectively like disabling the DRL option.

You could either wire the headlight bulbs directly to a fused power source (running new lines), and then implement a new headlight switch, or you'd need to install 2 new release, each connected to a new switch that could control power to each of the bulbs, but using your existing power wires. \

An example of the first options is like the Hella ValueFit Kit.