Bishop has appeared in 13 games with the Senators this season, posting an 8-5 record, a .922 save percentage and a 2.45 goals-against average.
"Ben came in here and saved us last year," Senators general manager Bryan Murray said. "We think he's an NHL goaltender that will have a good record going forward, but to be fair to him with Robin Lehner on the way up here and Anderson ready to go again we just felt it was unfair to one of them. This helps him I hope and it helps us."
The Senators acquired Bishop prior to the 2012 trade deadline after the Blues were forced into making a decision to clear the team's crowded crease.
"It's a little bit bittersweet," said Bishop. "I've developed some great friendships with the guys on this team and obviously it's a playoff team, but on the other side I'm very excited to go to Tampa."
Conacher, 23, has scored nine goals and 15 assists in 35 games with the Lightning this season. The five-foot-eight forward was signed as an undrafted free agent by the Lightning in March, 2012.
The Burlington, Ontario-native currently ranks second in NHL rookie scoring behind only Florida Panthers forward Jonathan Huberdeau. Conacher becomes the Senators' leading scorer upon acquisition.
"If we need anything we need a point-getter," Murray said. "I think he addresses one of those needs at least."
With Brian Elliott and Jaroslav Halak still under contract, the 6'7" Bishop was in danger of becoming a Group 6 unrestricted free agent this past off-season. The Senators acquired him in exchange for a 2013 second-round draft pick.
He is slated to become a restricted free agent at the end of this season, having signed a one-year deal worth $650,000 for this season.
Bishop was originally drafted in the third round (85th overall) by the Blues at the 2005 NHL Entry Draft. He has appeared in 36 career NHL games between the Senators and Blues posting a 15-13-3 record with a career 2.58 goals-against average and a .911 save percentage.