The move involving the 24-year-old left wing was among several waiver transactions around the NHL, as teams look to make roster and salary cap adjustments ahead of Wednesday's 3 p.m. ET trade deadline.
The five-foot-eight Conacher has suffered the dreaded sophomore slump this season, with just four goals and 16 assists in 59 games. He impressed as an undrafted rookie in 2013, with 11 goals and 18 assists in 47 games with Tampa Bay and Ottawa, adding three goals in eight playoff games for the Senators.
Bishop has gone on to star for the Tampa Bay Lightning this season, but at the time of last year's trade he was No. 3 on Ottawa's depth chart behind Craig Anderson and Robin Lehner. The Sens also received a fourth-round pick for Bishop, who, in general manager Bryan Murray's defence, had been traded previously by the Blues.
The pick was used to draft Swedish forward Tobias Lindberg last year.
The Sens on Tuesday also waived 36-year-old defenceman Joe Corvo, in his second go-round with the organization. Corvo has three goals and seven assists in 25 games with Ottawa.
The Florida Panthers also waived a pair of players in goalie Scott Clemmensen and forward Scott Gomez.
Gomez had just one goal and seven assists in 29 games with Florida.
The 34-year-old could be looking at the end of his NHL career, as his stock has continually dropped after signing a seven-year, $51.5-million US contract as an unrestricted free agent in 2007 with the New York Rangers.
Montreal assumed that contract in a trade with the Rangers, then bought Gomez out in 2012. The Anchorage, Alaska native played last season with San Jose.
Clemmensen has an .897 save percentage and 3.02 goals-against average in 16 games with Florida. It's his fifth season with the Panthers.
The other players waived Tuesday were Jake Dowell (forward, Minnesota), Corey Potter (defenceman, Edmonton), Derek Smith (defenceman, Calgary) and Trevor Smith (forward, Toronto).
Players waived can be claimed by other NHL clubs over the next 24 hours before being reassigned to the minors or bought out. With other players potentially available for trades ahead of Wednesday's deadline, claims could be unlikely.