Atletico drew 2-2 with the third-tier side in Thursday's Copa del Rey second-leg meeting, marking their third match without a win.
Progress to the last 16 was assured courtesy of a 3-0 first-leg triumph on the road at the start of the month, but Real Madrid's blistering form in La Liga has put the pressure on Simeone's men to find consistency in the league.
The champions can make a dent in Real's seven-point lead on Saturday as Carlo Ancelotti's side are in Club World Cup action this weekend.
But they will need to produce a far superior display to the one seen in midweek, when two Mario Mandzukic goals were cancelled out by Ruben Alcaraz's double.
Though Simeone did not make wholesale changes for the match, he did hand Ivan Perez a debut and also started fellow reserve-team defender Lucas Hernandez.
Both are likely to be left out against Bilbao as Atleti look to mitigate some of the damage that last Sunday's 1-0 loss to Villarreal did to their title bid.
Recent history favours the visitors, who won twice at San Mames Stadium last season in the league and Copa del Rey, completing a clean sweep of four victories over Bilbao in the 2013-14 campaign.
The Basque club were also in cup action on Thursday, recording a 1-0 triumph against Segunda B outfit Alcoyano to prevail 2-1 on aggregate.
Ernesto Valverde's men have now lost just once in their last nine matches in all competitions, helping them to the safety of mid-table and into third spot in their UEFA Champions League group.
But Bilbao have struggled for goals this season, scoring just 13 in 15 league matches, with Aritz Aduriz accounting for five of those.
Valverde made several changes for the Alcoyano match, including a rare start for second-choice goalkeeper Iago Herrerin, who is set to resume a watching brief as Gorka Iraizoz returns between the posts.
And, while finding the net has been an issue for the hosts, they have been impressive defensively, particularly on home soil.
Bilbao have conceded just four home league goals, with only Barcelona able to boast a better record.
