Peter Dreier, mayor of the district of Landshut, said he wanted to “send a signal” that Germany’s asylum policies could not continue as before.
The bus arrived in Berlin on Thursday evening. All those on board volunteered to make the journey, the council said.
Mr Dreier said he had informed Mrs Merkel of his bus plan in a phone call in October.
German government spokesman Steffen Seibert said in a statement that in Germany the state and local authorities were responsible for accommodating refugees, and they were provided with comprehensive support from the federal government.
“Berlin [meaning the state authority there] has agreed in this case to provide the refugees with the first night’s accommodation,” he said.
However, after at least an hour-and-a-half parked outside Mrs Merkel’s official residence, and with some uncertainty for those on board, the bus headed off.
Mr Dreier told Die Welt newspaper that he was not happy with the emergency accommodation offered by Berlin, so he was paying for one night’s stay at a guesthouse.
“What happens after that, we’ll see,” he said.
German reporters on board said the travellers had been unaware that the trip was a political statement – and some have criticised the mayor’s move.
“It is outrageous that he is exploiting those seeking protection,” said Bavarian Green Party co-leader Sigi Hagl. “Completely wrong,” she tweeted.
The mayor, who waved the bus off from Landshut, followed in a car after a meeting and was surrounded by media on arrival outside the chancellery.
“An end to the wave of refugees in not in sight, the country’s capacity of accommodation fit for human habitation is rapidly running low and I see no sign that new dwellings for immigrants are being built,” Mr Dreier, who represents the Independent Voters grouping, said in a statement.
Mrs Merkel had said she understood his concerns when they spoke by phone, and said he should give her office one day’s notice of the bus’s departure, the council said.
Ellmar Stoettner, a spokesman for the local council who travelled on the bus with the refugees, told the BBC that they would be offered a return journey to Bavaria if they so wished.
They were all happy to be on board and had made the journey having been fully informed of their options, he said. Fifty-one refugees had originally expressed interest in the trip.
The Landshut district has to house 2,100 asylum seekers, and that number continues to grow, he said. The population of the district – largely small market towns and villages – is 152,000.