Bowditch saw his 65th-minute spot-kick saved by Sam Walker as Gavin Williams' first-half goal ensured a fourth win in five games for the Glovers, who had Dean Parrett sent off on the stroke of half-time.
Both teams ended the match with 10 men as Dons midfielder Stephen Gleeson was shown a straight red card in stoppage time for violent conduct.
The Dons controlled the first half and Jay O'Shea curled a good early chance over the bar before Adam Chicksen fired narrowly wide after beating three Yeovil defenders. But Williams put Yeovil ahead against the run of play four minutes before the break, collecting Lawson D'Ath's mis-hit shot before beating Dons keeper David Martin at his near post from a tight angle.
Parrett was given his marching orders in the 45th minute after picking up his second booking in quick succession for a needless foul on Shaun Williams.
Bowditch then had his penalty well saved by Walker after his cross had been handled in the box by Luke Ayling. The Dons piled forward late on but Daniel Powell and Mathias Doumbe both missed good chances before Walker denied Alan Smith with a brilliant point-blank save at the death.