Using the super-soft tyre, Bird lapped the Principality in 1m21.512s, leading a Russian Time one-two ahead of team-mate Tom Dillmann, who was 0.057s slower.
Bird rates the Monaco track as his favourite on the calendar, and won here in Formula Renault 3.5 last season.
Mitch Evans was best of the rest for Arden in third, almost a quarter of a second off Bird's pace. Jolyon Palmer was fourth fastest for Carlin, but was unable to break into the 1m21s bracket.
Barcelona poleman Marcus Ericsson was fifth fastest for DAMS, ahead of Johnny Cecotto Jr, Fabio Leimer, Felipe Nasr, Rio Haryanto and James Calado, who suffered an overshoot at Ste Devote near the end of the session.
The drivers were very well behaved in the session, with only a couple of moments to report. Local hero Stephane Richelmi spun at Rascasse, and then stalled as he attempted to recover, ending the session 19th.
Nasr had the nearest of misses at the Swimming Pool, while championship protagonists Leimer and Stefano Coletti suffered overshoots; Leimer at Ste Devote, Coletti at Nouvelle Chicane. Kevin Giovesi also slid to a halt at Rascasse.
Championship leader Coletti, who hails from Monaco, ended the session down in 17th. Barcelona feature race winner Robin Frijns was even slower, down in 20th and 2.1s off the pace.