According to the airport, the development, part of a "masterplan to 2040", was forecast to provide more than 37,000 jobs in the South West and South Wales, plus another 1,000 roles at the airport itself.
A spokesperson said the proposals aimed to "meet the strong and growing demand of people in the region".
The plans included a larger terminal building, improved onsite catering facilities, a new hotel, a bigger runway for long-haul aircraft, improved transport capacity on the A38 and more parking.
Mr Lees said there had been a rise in travel since the pandemic: "The masterplan will look at what further development might be required to meet this growing demand for air travel and we’d welcome input from people to help shape our plans."
He called the growth "responsible", explaining the airport, which is based in North Somerset, was investing more than £400m on improving customer experience and reducing the Airport’s carbon emissions, with aims to achieve net zero in its operations by 2030.
"Meanwhile, we are also committed to working with partners in our region on aviation decarbonisation," he said.
The increase in passengers up to 15 million per year, would mean about 100,000 aircrafts movements per year from the airport, a rise of almost 15,000.
Jackie Head from Bristol Airport Action Network, called the latest plan "very disappointing".
"It doesn't consider the needs of local people, it doesn't consider its climate impact."
She said the airport's projected impact on economy and jobs was "misleading", explaining the network's research showed the airport regularly "massively over-emphasises how many new jobs or what new money will be produced".
Ms Head said studies showed more tourists leave the country to spend money than come to the UK, "so it's not good for the economy, it's not good for local people".
"It's also a reality that in the next 10, 15, 20 years, there's going to need to be a pulling back of aviation" because of the need to reach net zero targets, she added.
The consultation period runs until 31 January 2025, with a planning application set to be submitted to North Somerset Council next year.
