Former City striker Daniel Nardiello opened the scoring for the Shakers in the 15th minute, but David Wheeler levelled with his first goal in professional football four minutes before half-time.
Nathan Cameron's thumping header put Bury back in front, but Tom Nichols rescued a point for Exeter 13 minutes from time.
"At the start of the game I wanted a win but, all things being said, we have had two draws this week. It is not a bad start after a rotten month and five defeats in November," Tisdale said.
"We have these games here and when it is a bright day, I am desperate for us to win the toss and not have to play into the sun because it makes the first half a lottery. It is really difficult and made our players edgy.
"We didn't quite have the connection we needed in the first half, our passing was adrift and we weren't great.
"Our goalkeeper (Artur Krysiak) made a mistake with the goal, he doesn't make many, but we have come back twice and responded.
"We know our plan and an idea of what we are trying to do and I am glad we practice it because we came back and got the point."
- Sports & Recreation
- Daniel Nardiello