Mrs Bolger took the seat that belonged to council leader James Mills in Witney East, beating her Conservative opponent Ron Spurs by just 10 votes in the closest result of the night.
European Union citizens are able to vote, unlike in general elections, and some campaigners have been pressing Brexit as an issue.However, questions of local tax rates, bin collection and the state of the roads also dominate many campaigns, making analysts wary of drawing too many national lessons from the results.Polls opened at 7am (0600 GMT) and close at 10pm, and although some results will come in overnight, the full picture will not be clear until Friday.
There are no local elections in Scotland, Wales and Northern Ireland. The rest are being counted during the day on Friday with results expected during the afternoon. However, a parliamentary by-election for the Westminster seat of West Tyrone is taking place.
In a busy night of local election results across the region, the biggest news comes from Trafford where Sean Anstee's Conservatives have lost control of the council.
Conservatives may be boosted by Ukip's decline in the polls, with targets like Basildon or Great Yarmouth potentially up for grabs if the Eurosceptic party performs poorly.
Of the 20 seats being elected, 4 are now held by the Conservatives, 9 by Labour and 7 by the Liberal Democrats. They will be hoping to appeal to Remain voters in parts of London they used to control but leader Sir Vince Cable has warned against expecting "spectacular progress".
They are made up of varying numbers of seats, and run by any party that has an overall majority of those seats.
"1.67 percent of all voters across the five pilot areas were unable to vote because they did not have the required ID to vote".
"There, at the moment, isn't really very much for the Labour Party to crow about.it basically has come away frankly empty-handed relative to the expectation that it at least helped to build up", Curtice said.
The scheme had been already criticized by the Electoral Reform Society, which said the measures would affect not only the elderly, but homeless, disabled, young people and people from ethnic backgrounds.
Mr Mills, who won a seat in the Bampton and Clanfield ward, said there were a number of reasons for this, including people using the elections to express dissatisfaction with the current Conservative Government.
"This is a pilot, an evidence-based approach, and obviously we will consider the pilot and decide the best way to go forward".