Rory Fallon scored Swindon only goal in the second half, before Bideford equalised shortly after.
Swindon team was: Jordan, Jenkins, O'Hanlon, Ifil, Smith, Shakes, Pook, Wells, Nicolau, Thorpe and Cureton.
Swindon now stop off at Taunton Town on their way back from devon on Thursday evening, before travelling to Crawley Town on Saturday.