Can a bike with an internal bottom bracket be retrofitted to have an external bottom bracket?
The external bottom bracket uses the same thread size and shell width as an older internal BB. They were specifically designed to allow use in a standardized frame without redesign. 

They do require a new crank set, and depending on the model, and what is on your current bike, that may mean the purchase of extra components in order to be compatible with the correct number of gears/width of chain. If you are going from 9 speed MTB to 9 speed MTB components, for example, a like for like change, then it should be just the crank set and BB that change.

An external BB is also designed to fit on either a 68mm or 73mm shell. They are universal, as long as you dont have a pressfit BB, or an Italian thread BB. Similar crank sets are available for non-english thread BB's, but it must be designed for your frame's BB shell type specifically.