Sounds like a heat problem with either the bulb itself or likely the connector. Once I found a bulb had a dry solder joint. It would stay lit for a short time and go out. Then it would come back on a few minutes later, then heat up & go out.
Was a cheapy and I spotted the solder was dry, a grey matt colour as opposed to silvery shiny coloured.
But if it's taking ten minutes, sounds like the heat is taking time to build so likely the push on connector at the back of the bulb. Check for grotty green/yellow build up.
Remove from bulb, spray with contact cleaner, use brass wire brush to get grot off and if you have a nail file, clean the contacts before replacing on the bulb pins.