Do telogen effluvium hairs have a white bulb?

Yes, they do. There is really no such entity as a telogen effluvium hair. The proper terminology would be "a telogen hair obtained from a person who is experiencing a telogen effluvium." Hairs that are shed in androgenetic alopecia are telogen hairs. Hairs that are shed in a telogen effluvium are telogen hairs. Hairs that are shed normally are telogen hairs. They all have a white bulb.

Hair colour is formed by melanin deposition. Effluvium is unlikely to change the colour of shedding hairs. The bulb of any hair may not be pigmented and therefore appear colourless.Loss of hair shaft pigmentation or poliosis is part of normal hair ageing. There are many theories regarding aetiology but one of the leading causes is thought to be oxidative stress related to build up of hydrogen peroxide. Prevention and treatment options therefore could include anti-oxidants. 

Telogen effluvium hairs, when they shed, like any shedding hairs will have a colorless bulb. These hairs may pull out easily