A subgroup of dwarf galaxies have characteristics of a possible evolutionary transition between star-forming systems and dwarf ellipticals. These systems host significant starbursts in combination with smooth, elliptical outer envelopes and small HI content; they are low on gas and unlikely to sustain high star formation rates over significant cosmic time spans. We explore possible origins of such starburst transition dwarfs using moderately deep optical images. While galaxy-galaxy interactions could produce these galaxies, no optical evidence exists for tidal debris or other outer disturbances, and they also lack nearby giant neighbors which could supply recent perturbations. Colors of the outer regions indicate that star formation ceased > 1 Gyr in the past, a longer time span than can be reasonably associated with the current starbursts. We consider mechanisms where the starbursts are tied either to interactions with other dwarfs or to the state of the interstellar medium, and discuss the possibility of episodic star formation events associated with gas heating and cooling in low specific angular momentum galaxies.