I'm by no means a Bournonville expert, but I'll try my best to give you an idea of the style and point you towards some good resources.
The best place by far is the Bournonville Website, http://www.bournonville.com/
, which has wonderful articles about Bournonville, the style, the dancers (and dance types). Click on the link on the left for "The Style" and you will find a series of article on the style, including a great article, 'Positions and Stylistic Characteristics" on the positions with links to pictures of each position. There are also articles on the typical male and female dancers.
It's not easy to put the style into words (the above website does a much better job than me), but I think 'fluidity' and 'delicacy' are a part of it. Bournonville technique is very demanding, in that it's all about the effort not showing. There's a great emphasis on the epaulment (how you hold your arms and upper body) and the head is almost always tilted slightly down at an angle. In Bournonville's choreography there is little rest - instead of having the dancer walk back to get room for another sequence, the dancer will have a series of steps back acrosss the stage. There is also a great emphasis on fast legwork - beats etc., but without losing the fluid, stage-skimming look.
For me, the style is illustrated most perfectly in the flying grand jete attitude croisee en le air (grand jete with legs bent in attitude) that marks Gennaro's entrance onto the stage in 'Napoli'. It has to be light and airy, but cover an immense amount of space and not be heavy on the landing. It's not as flashy nor does it often look as spectacular as the tours and spins of other ballets, but it's just as challenging. I first began to appreciate the difficulty when sitting on the studio floor watching men's class at the Royal Danish Ballet looking UP at the dancers as the did some short Bournonville Class excerpts. The height and distance that men like Thomas Lund cover in the move, while still landing softly and lightly, is just amazing. And the sheer speed of their legs in the beats - things like that often aren't so apparent from out in the audience.
I'm not sure it's really possible to describe the perfect Bournonville dancer, because there is so much diversity in Bournonville's roles. Thomas Lund, who is one of the best Bournonville dancers today, is on the short side and slender. But Mads Blangstrup, who also dances many lead roles is quite tall, though also slender. Then you have dancers like Peter Bo Bendixen, who is tall, but more solidly built, who has excelled in different roles, and is a fabulous character dancer. And Kenneth Greve who is very tall and solid, but also dancers a wide variety of roles.
The women also vary, just as in any other company, and thus dance in different roles. So, I think if you are going to describe the attributes needed to be a Bournonville dancer, it would be patience, diversity and good acting skills. It takes years to perfect the style - the Danes start as 8-9-10 year old children in the Royal Ballet School - and it takes as time to learn the distinctive mime skills as it does the technical skills. You really can't go far as a Bournonville dancer unless you are convincing in the roles, which means being comfortable with mime and understanding the history behind the ballets/characters. And then it has to go into one package, and look effortless.
Gotta run to my own ballet class...if you want more detail on something I mention etc., please post!