The on loan Arsenal star has been speaking to West Ham's official site about his hopes for the game and the season in general.
It set them up perfectly for their first home match against Leicester City in what is the club's last ever season at its Boleyn Ground home of 112 years.
The efforts to ensure Upton Park was a fortress for the momentous season fell at the first hurdle, though, with the Foxes inflicting a 2-1 defeat on Bilic's side.
It was a first game of the season for Jenko' as he is known to his teammates as he was unable to play against the Gunners due to Premier League rules.
He didn't offer his usual threat as an attacking force against the Foxes as he shook off the summer ring rust.
'Professional performance will bring three points'
But now he has told West Ham's official site that he is focused on producing his best against the Cherries and has called on more professionalism to get a first win of the season at the Boleyn Ground.
"We need to win these games at home – last week was a big disappointment and we need to bounce back from that," Jenkinson told whufc.com.
"We will need to put in a good performance and a professional performance if we are to get the three points.
"We started well in the first ten minutes against Leicester last week, but then seemed to sit back a little bit and not press as well as we can."
West Ham need Jenkinson in top form
Jenkinson, who has to deputise in goal for Adrian after his sending off in the dying moments against the Foxes, was one of West Ham's best players last year both offensively and defensively.
Hammers fans were hoping to see him signed up permanently this summer but Arsene Wenger dashed any hopes the east Londoners had of luring him across London full-time by handing the pacy star a brand new five-year deal.
Instead co-owners David Sullivan and David Gold were forced to settle for another season-long loan.
Now Slaven Bilic will be hoping swashbuckling defender is quickly back to his best, something Jenkinson is aiming for as soon as possible, starting with Bournemouth.
He added: "I’ve had a couple of 90 minutes under my belt so I’m looking to be flying now as I should be fully fit.
"I’ve got to express myself and play to the best of my ability."