With the ilk of Kysaiah Pickett, Charlie Spargo, Jake Melksham and Alex Neal-Bullen all preferred as offensive options by head coach Simon Goodwin, Bedford's opportunities within forward 50 have proven few and far between.
Bedford laced the boots on 16 occasions throughout the 2022 season, however, the 22-year-old failed to see action in eight fixtures, instead fulfilling the duties of medical sub.
Though Bedford is said to have a three-year deal to remain a Demon available to him, the ability to replace outgoing Giant Bobby Hill in charcoal and orange appears a prospect too strong to refuse.
“While we are disappointed that we will be losing Toby, we understand and respect his decision to pursue further opportunities,” Lamb expressed in a club statement.
“We will now work with the GWS Giants to facilitate a suitable trade.
“We thank Toby for his contribution and commitment to the club over a number of years.”
Essendon also held a desire to lure Bedford across town, with the Dons said to be keen to draw further forward talents through their door.
Bedford will depart AAMI Park after four seasons, 18 games and nine goals in the red and the blue.
The Melbourne Grammar graduate joined Melbourne with the 75th pick of the 2018 National Draft after rival clubs failed to make a bid for his services.
At present, GWS holds an arsenal including picks 3, 21, 40, 58, 60 and 76 in an effort to land the livewire.