Victory would make it five wins and one draw from the first six league matches, matching their opening to the 1969/70 campaign.
The Toffees have turned around impressively under new boss Ronald Koeman after a woeful end to last season.
In 1969/70, the club went on to claim the First Division title, and they could climb to the top of the table if Manchester City lose at Swansea, b ut captain Phil Jagielka is not getting carried away
He told evertontv: "It's been a while since we've enjoyed looking at the league table but we are not looking at other people's results yet
We need to keep going, keep grinding out the wins.
"If we have a look at the table 10 to 12 games in, that will give a rough idea of how everyone's starts have gone
We are only five games in - a good five games - but if we don't do well between now and Christmas then the start doesn't count for anything."
Things have been going well at both ends of the pitch in the league, with Everton conceding only three goals and scoring 10.
Four of those have come in the last two games from Romelu Lukaku, who should return from a toe problem that forced him to miss the EFL Cup defeat to Norwich on Tuesday.
"We've kept in games and then won games when we've not played as well as we could have done," said Jagielka.
"With the attacking talent we have got - Romelu Lukaku and Yannick Bolasie have done fantastically well these last few games - it's up to us at the back to keep the opponents out so they can get the headlines and win the game for us."
Tuesday's loss was the first hiccup for Koeman since he joined the club from Southampton in the summer.
Bournemouth have only taken four points from their five games but the Dutchman expects a tough assignment on his first return to the south coast.
He said: "It's a strong team, a team that likes to play football from the back; aggressive, some good quality players
They had a very good season last year and it's a difficult one.
"We have had a good start to the season, maybe better than everyone expected
But we have a strong team."
One of the players to have stood out is midfielder Idrissa Gueye, who was signed from Aston Villa in the summer.
"The adaptation of the player did not take long," said Koeman
"From the beginning he was comfortable
He puts a lot of energy on the pitch, and not only energy but quality on the ball.
"It's a great signing
This is only his second season in the Premier League
He can improve
He will be stronger and more clever and that's all about experience."
Source : PA
Source: PA