The bus, which was empty at the time, was hit by a tree branch on the A4500 Wellingborough Road, between Ecton and Earls Barton, at about 7am.
The bus was substantially damaged and part of its roof was torn off.
Several roads in and out of Northampton were also hit because traffic lights had failed.
Ann Smith, a resident of Brownlow Court, Lumbertubs, Northampton, said: "It was terrible. I was absolutely petrified.
"I could see trees bending down in the wind. I watched it through the window - I heard a loud boom and the trees came down."
In Mounts Court, Lumbertubs, branches had snapped off trees, with one landing on the roof of a house.
Branches were also overhanging a house in Bitten Court and strong winds blew a tree into the road near Abington Park.
Police received reports of 15 affected roads where felled branches and leaves had caused disruption.
Several trees were reportedly blown down in Bugbrooke.
The Met Office said a severe weather warning was in place for Northamptonshire and Leicestershire and motorists were being advised to drive with caution.
Chron reader Sarah Malone, 33, said she watched in horror as the tornado went through her street in Keyham Close, Blackthorn, Northampton.
The primary school teacher said: "It started off as normal strong winds but they didn't relent and blew the tiles off the rood. I couldn't see anything at first, it was just the noise and wind gusts. Everything was just a blur.
Did you suffer in the bad weather? Click here to tell us your story or send pictures of the damage"I hate bad weather and I looked out this morning and my legs just went to jelly. We've had strong winds before but I've never experienced anything like that before, causing so much damage so quickly.
"I was lucky - my conservatory roof did lift but it didn't come off. I don't think we're really prepared for this kind of weather here."
Andy Cooper, of Tinsley Close, Cherry Lodge, said: "I was lying in bed at 6.55am. The house and bed shook and rumbled for about 10 seconds.
"I jumped out of bed, looked out of the window and pressed my hands against it to feel the glass moving in and out, which alarmed me because it was new double glazing fitted recently.
"Next door now has a hole in the roof and several tiles missing. I have never seen anything like it."
Northampton hit - but what is a tornado? Click here to find outCaroline Fromant from Glassthorpe Farm in Harpole, woke up to find several trees had damaged the fences keeping in the cattle.
She said: "It's amazing. They are big conker trees that have been bought down after it hit at about 7am. There are lots of boughs all over the road and the trees have come down on the fencing.
"I've got cattle in there and they're roaming the fields now. They're very skittish this morning because of it all, and the damage will cost a couple of hundred pounds, but we're just concerned with getting the trees off the road.
"It's quite amazing; there are conkers all over the road."
The violent storm went on to hit Luton at 7.30am, ripping through gardens and tearing tiles off rooves.
Twenty homes were hit by a tornado in Farnborough, Hampshire, at around 8am, pulling a roof off a garage and uprooting trees, the fire service said.
A spokesman for the Met Office said weather conditions conducive to tornadoes were travelling across the country.
A Hampshire Police spokeswoman said that up to 10 houses were damaged, including some with severe structural damage when the tornado struck in Farnborough.
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