The Cherries won the Championship title last season and will feature in the top flight of English football for the 2015-16 campaign.
Jenas, who has loads of Premier League experience, is looking forward to watching Eddie Howe’s side in action this campaign and has a piece of advice for them.
“I really enjoyed watching Bournemouth last year and their style of play probably suits the Premier League best out of the three promoted teams,” the 32-year-old told BBC Sport.
“But that pretty tippy-tappy football they play won't pay-off if they don't put their chances away.
"That is something you can get away with in the Championship because you know other chances are going to come.
"In the Premier League it is the total opposite, so they will need to be more clinical.”
Can Bournemouth stave off relegation?
Bournemouth surprised many last season, as they won the Championship title ahead of the likes of Middlesbrough and Derby County.
The Cherries are being tipped by many to go back down straightaway, and that could well turn out to be the case.
However, it must be noted that Bournemouth have some good players and Howe has shown that he is a very good manager.
While the Cherries are going to struggle for points and wins away from home, if they have a strong form at the Vitality Stadium, then they will be able to survive.