"Everyone is safe and well but our message to the public is just be wary on the roads," Loughrin said.
"It's very windy and wet so drive within the conditions."
The Waikato has been buffeted by strong winds and rain today along with other parts of the North Island.
Loughrin said the bus was damaged in the incident and not able to be driven to the destination, about 90 minutes away.
Another bus had been arranged to transport the tourists to Waitomo.
"The tourists will shortly continue on with their travel plans in New Zealand."
In the Rodney district a downed tree blocked SH1 this morning causing a queue of traffic in both directions near Pūhoi.
The tree was cut up by a man with a chainsaw and moved after 9am.
In Auckland residents had been dealing with power outages as the city was battered by gales earlier today.
MetService issued a strong wind warning for Auckland, saying southwesterly winds could approach severe gales in exposed places.
There were reports of power out in Mairangi Bay, Browns Bay, Rothesay Bay, Windsor Park, Sunnynook, Titirangi, Swanson, and Glen Eden this morning.
Vector said there were a number of outages in the Auckland area and the heavy weather was causing delays in fixing the problems.
And a tiny home being towed on a trailer overturned on SH20 at Mangere Bridge around noon.
An NZTA spokeswoman said the vehicle and trailer had jack-knifed into the southbound bus lane, but the incident did not badly affect traffic.
Meanwhile MetService is predicting the weather will turn cold overnight as a cold front moves across the country.
Meteorologist Claire Nixon said on the MetService weather channel the cold air would come up the country from the south bringing strong southwesterlies.
Temperatures are expected to dip below zero in southern parts of the South Island and the central North Island, though Auckland would only go as low as 8C.
"However as we head into Sunday there is a ridge of high pressure out there to the west that's going to be starting to move on and that will start to settle things down later in the weekend."