Bradbury admitted the Frenchman had done his chances no harm after his equaliser sparked Monday's comeback victory over Bristol Rovers.
A product of the Le Havre academy, Baudry signed a deal until the end of the season after having his contract with French outfit Troyes cancelled by mutual consent in January.
He described as a dream the chance to ply his trade in England and the centre-half could get the option to extend his stay after impressing manager Bradbury.
Despite being restricted to one start and two substitute appearances since his arrival, Baudry's work has not gone unnoticed.
Bradbury told the Echo: He has had to be patient but is very professional. He does everything 100 per cent right all the time.
Even if he is not involved or not playing, he is always doing the right things. That goes a long way because when he is called upon he is raring to go, ready, knows everything we are trying to do and fits in very well.
He is always looking to improve, which is great for me. He is always asking questions because it is a different game from the one he is used to in France.
He is a joy to work with and I have to drag him off the training pitch at times because he wants to stay out all the time. He is a great lad.
Bradbury's primary focus is on Cherries' attempts to seal a play-off place with his side sitting in sixth position going into the last two games of the League One season.
When asked whether he would be looking to try to keep Baudry beyond the end of his current deal, the Dean Court boss added: We have got to concentrate on the job at hand, but he hasn't done himself any harm from what I have seen of him, especially on Monday.
I like him as a lad and as a player, so I will probably address these things in the next couple of weeks.
Baudry scored his first goal in English football after coming on as a substitute in defensive midfield against Rovers. Bradbury added: I thought he was very disciplined. He passed the ball well and scored a good goal. I think that could be a position for him in the future, as well as centre-half.
Cherries are offering free travel to supporters who buy tickets for Saturday's game at Hartlepool United. As part of the deal, the club is also offering fans a hot drink and bacon roll from 5am. To buy a match ticket and book a seat on a coach, visit the club store or phone 01202 726338.