Bird, 29, took 19 wickets in the competition in a three-month spell with Hampshire last season.
"I got a bit of a taste for it and didn't play as well as I'd have liked. I feel that I've got a point to prove to myself more than anything," he said.
He is available for the opening 10 matches of Notts' county campaign, starting against Surrey on Sunday.
Bird, who has taken 21 wickets in five Tests for Australia, is eager to begin the season at home at Trent Bridge, having been overlooked by national selectors for the first Test of the 2013 Ashes series at the venue.
And he is determined to help Notts get off to an improved start to the four-day campaign, having won two and lost four of their opening 10 County Championship matches last summer.
"I just want to contribute, get Notts off to good start and win as many games of cricket as we can," Bird told BBC Radio Nottingham.
Nottinghamshire seamer Jackson Bird says he has returned to the County Championship on a personal mission.