The 20-year-old Welshman, who joined the Grecians from Leicester last summer, has made just three first-team appearances this season and could play in up to nine matches for the Romans.
Fellow striker Tom Nichols has just returned from a loan spell with the Blue Square Bet South side which saw him play seven times for the Twerton Park outfit.
"A number of our young prospects have gone out on loan this season and returned with an increased level of maturity that comes with playing first-team football," manager Paul Tisdale said.
"Elliott is a really bright young man with bags of potential, and now he has the same opportunity to play regularly and we'll be monitoring his progress with Bath.
"We will look forward to welcoming him back to Exeter soon."