They're probably not as popular as the HPS to MH bulbs, but they do exist. If there's a mechanism that's needed to ignite the gases within the arc tube, then it must be built into the bulb...at least, on the one that I remember seeing.
Thats why I use the term unlikely rather than "you will not" or "there is no such thing" since anything electrical items dedicated to one system will sooner or later have a conversion system designed by a budding engineer looking to get a good mark on a thesis.

Two seconds on google give you these ones.

Buy HID Metal Halide & HPS Conversion Bulbs Here!
Buy 250W EYE Hortilux HPS Conversion Bulbs Here!

but from them you will see physical shape may then cause issues with fitting in some reflectors. Like all the will this bulb work with X system questions there is a lot of maybe but maybe not unless you are using a system which is widely used, has been tried using the adaptions your asking about & has been posted somewhere for people to read about.

The best answer IMHO is if you already hae the lighting system & ballast do a search on your make & mdel enclosing the whole lot in "" quotes. This will give an idea of what people have already used it for.

If you don't already own the MH ballast system then whats the pont in fighting the flow of electricity to just be different you might as well get the most common system & benefit from the reduced purchase costs.