Verstappen was third, just 0.125s behind Bottas, with the Dutchman to start behind Hamilton on the long run down to Turn 1.
Verstappen has extra incentive to finish the season strongly, with the 23-year-old just 27 points behind Bottas in the drivers' championship standings with three races remaining.
After handing Red Bull its first top-three start in Bahrain since 2014, Verstappen didn't rule out his chances of victory.
“I definitely do think (Mercedes) picked up their pace today so even tomorrow it will be, let's say, hard to beat them, but we have different tyres available… so let's see if that works to our advantage or not,” said Verstappen, who was fastest in Free Practice 3.
“I just hope that it will be an exciting race, I think that will be the most important.
“My lap was pretty good… just lacking a bit of rear grip in the lower speed corners for my liking, but overall I think it was quite a decent qualifying.
“Let's see how we will go tomorrow in the race, because it's very hard on tyres, so I hope we made the right compromise for that.”
Bahrain qualifying marked the ninth time in the last 12 races that Hamilton, Bottas and Verstappen featured in the top three.
Verstappen still remains the one without a pole in 2020, and was disappointed Red Bull couldn't close to gap to Mercedes at the Sakhir circuit over one lap.
However, with Red Bull team-mate Alex Albon recovering from a heavy Friday crash to qualify a career-best fourth, Verstappen will be hoping for company should he take the fight to the Silver Arrows.
“You always want more but it's more important to stay realistic and work on the little things,” Verstappen said.
“The weekend in general was pretty positive. Just lacking a little bit too much in qualifying… I don't know why that was, exactly.
“Let's see what happens. I just try to focus on myself, try to stay close to the Mercedes cars and then I'll see if somebody can follow us.”
The Bahrain Grand Prix will commence at 01:10 Monday AEDT.