The five-year contract will see the Leeds firm operate private hire services to and from the UK’s ninth busiest airport.
The business, which also operates from Leeds Bradford, Manchester and East Midlands airports, is expected to boost its headcount from 60 to 85 staff ahead of its April 1 start date.
It will also grow its driver numbers to around 700 to accommodate the additional location.
Arrow Cars chairman David Richmond told The Yorkshire Post that the firm is looking to grow further.
He said: “We’re investing huge sums of money in our IT, technology, office, staff and, of course, cars.
“Bristol is an airport of 6.25m passengers, it flies all over the world. We’re a Leeds company, so we’ll remain headquartered in Leeds, so this will mean more jobs in the city in terms of management and administration staff.”
Arrow, which offers app and online booking in addition to phone and face-to-face services, is currently in negotiations with another three airports.
Mr Richmond, who is a former Leeds United director, said the potential locations included “significant” airports that would be a major boost for the firm.
Arrow already has drivers based all over the country. “We’ve literally got drivers everywhere: provided you’re going to or from one of our main cities, we will have drivers nearby,” he said.
Private hire firms have traditionally remained local businesses due to the complexity of licensing regulations, which differ between councils.
However, Mr Richmond said while there are challenges in operating in several locations, they are “workable”. “There are different rules and some rules in some areas seem nonsensical and difficult, but we are fully compliant,” he said.
“We register and obtain an operating licence for each location. Effectively each area runs independently of each other.”
Following the launch of US taxi app Uber in Leeds in November 2014, Mr Richmond suggested the city could see “unrest” in the taxi industry. Uber has faced protests in other locations.
However, Mr Richmond hailed the firm as “fantastic”, adding that Arrow’s Leeds business has grown 26 per cent since November.
“They’ve grown the market and it’s been great for us,” he said.
“This is a local company, but we’re competing against the giant monoliths from San Francisco and succeeding,” he added.