In most PAPIs (i e all I've seen, and that's a fair amount) there is no 'red bulb' and 'white bulb'. You have one projector light in front of which sits a red filter, essentially a red glass pane. Change the colour temperature of the bulb and the colour of both red and white will change.
A good PAPI unit will have a transition zone of less than 0.05 degrees between fully red and fully white. Poorly maintained PAPI units will quickly go well above this, and you may end up with transition zones bordering on 0.20 degrees. With 0.17 degrees being the nominal difference between on glide path and a unit changing colour for a stand-alone PAPI, that's a lot.
Wide transition zones are usually caused by dirty lenses, dirty or worn glass panes in the units, improperly levelled units, improperly installed or seated filters or condensation which has not yet evaporated in a newly turned on PAPI box.