"It’s only practice but it was a lot more fun than normal," the 2009 world champion told reporters after clocking the third best time. "No problems today reliability-wise.
"There will be cars that will slip in between us tomorrow but you have got to say that it was a good day for us -- the best day for a couple of years -- so a positive start," added Button. "It is fun to have a car that is enjoyable to drive."
McLaren have not won a race since 2012, when Button triumphed in Brazil at the end of that season, and last year slumped to their worst ever showing in the Formula One championship with just 27 points.
The new partnership with Honda resulted in multiple engine failures and morale-sapping grid penalties, but the signs this year are that reliability has improved and the car is more competitive.
The sport's most successful team after Ferrari, with 182 wins, still failed to score a point in the Australian season-opener two weeks ago with Fernando Alonso suffering fractured ribs in a huge crash and Button finishing 14th.
The Spaniard was ruled out of Sunday's Bahrain race after failing a medical.
"I have just been speaking to him but I am sure his ribs have suddenly got a bit better," Button joked, feeling for the Spaniard who has remained at the Sakhir circuit to assist Belgian stand-in Stoffel Vandoorne.
Button said the team had done nothing unusual to the car and hoped for further improvement on Saturday, with a real hope of making it into the final phase of the much-criticised new qualifying format.
"When you are third in FP2 (second practice), and it’s not because of changeable conditions or anything, then you have to think about getting into Q3 (the final phase of qualifying). That has to be the aim," he said.