More than 1,000 drivers and engineers were set to stage the walkout on Bank Holiday Monday in a dispute over rosters.
It was supposed to be the second day of strike action after Unite members at Tower Transit took action on Friday.
It said it decided to suspend Monday's industrial action after "solid support" for Friday's protest.
A spokesperson said it wanted to give the company time to "reflect and respond".
Transport for London said Tower Transit operated less than 5% of the bus network.

The top seeds defeated Australia's Dylan Alcott and South Africa's Lucas Sithole 6-0 3-6 6-2.
"It's an amazing feeling and a lovely end to a tough couple of days," said 24-year-old Lapthorne.
Meanwhile, fellow Britons Jordanne Whiley and Gordon Reid both reached their respective doubles finals.
Whiley and Japanese partner Yui Kamiji stayed on track to retain their women's doubles title after the Grand Slam-winning pair defeated Germany's Katharina Kruger and Dutchwoman Sharon Walraven 6-4 6-3.
In Friday's final they will face Dutch second seeds Jiske Griffioen and Aniek van Koot who they beat in the Roland Garros, Wimbledon and US Open finals last season, although the Dutch pair won their most recent encounter in the Sydney International Open.
"I'm really happy to make the final, but it wasn't my best day," said Whiley. "I certainly need to play better in the final."
Reid will contest his second Australian Open men's doubles final after partnering Argentina's Gustavo Fernandez to win their semi-final against second seeds Joachim Gerard of Belgium and Maikel Scheffers of the Netherlands 6-1 7-5, having come from 2-0 down and 5-3 down in the second set.
"I'm delighted to be back in the final after a good solid performance from us - we're pleased how we battled through the second set," said Reid, who lost in last year's final.
Reid and Fernandez will play defending champions and top seeds Stephane Houdet of France and Shingo Kunieda of Japan in Friday's final.
Earlier on Thursday, Lapthorne saw his hopes of a place in the quad singles final fade when he was edged out 6-3, 7-6 (7-4) by Sithole in his second of three round-robin singles matches.

An uplifting Six Nations featuring wins over Italy and France ended with a 35-25 defeat by Ireland on Saturday.
Two quick Irish tries while the Scots had a man in the sin-bin proved costly.
"The top teams in the world simply don't have flat halves like we did. They don't come out and start slowly," Gray told BBC Scotland.
"I hope we can achieve that winning habit, and every time we take the field, we start with a bang."
Gray's second-half try in Dublin was one of 11 Scotland scored in the tournament, surpassing their previous best Six Nations tally of nine in 2000.
Their 25 points in defeat was the most they had managed in Dublin for 32 years, contributing to an overall haul of 122 from their five matches, the first time they had passed three figures in the Six Nations.
"I think there's been progress," added, Gray, echoing the sentiments of captain Greig Laidlaw and hooker Stuart McInally.
"Certainly, looking at last year's tournament, we didn't manage to win a game and this year we won two and came very close in two.
"We finished well and we'll take a lot of positives from the championship.
"We've always said that it's a talented group, it's a group that can do things and we're building towards something."
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Stuart Hogg, who scored a stunning solo try in Dublin, and Duncan Taylor, who enjoyed another strong outing after a brilliant individual try against France, have been nominated among 12 players for the Six Nations player of the tournament award.
England trio Billy Vunipola, Jonathan Joseph and Jack Nowell, Wales duo George North and Gareth Davies, Ireland's Jonathan Sexton and Conor Murray, France pair Guilhem Guirado and Virimi Vakatawa, and Italy captain Sergio Parisse are the others.
A planned bus drivers' strike which threatened to disrupt Notting Hill Carnival has been called off.
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Britain's Andy Lapthorne won his fourth Australian Open quad doubles title after he and world number one David Wagner retained their Melbourne crown.
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Lock Richie Gray says Scotland can't afford flat periods and must start every game 'with a bang' if they are to develop into a world-class team.