A private investor who criticised board members for not buying more shares in the placing completed by the oil and gas company last month, Tim Kempster, asked: "Isn't it best to hoist a 'for sale' sign and put us shareholders out of our misery?"
Chief executive Kevin Hart told the meeting the Africa-focused company had had a couple of challenging years in terms of its share price performance.
Mr Kempster noted not all directors bought enough shares in November's 45p per share placing to maintain their percentage holding in the company.
"You have said it is an incredible resource; why would you give up some of the upside and allow yourselves to be diluted?" he asked the board, referring to Bowleven's acreage containing finds off Cameroon.
Mr Kempster added: "It sends an enormous message to the market that directors don't have faith in the resource."
Mr Hart had told the meeting he felt the pain as much as any shareholder after spending around £1.8m on Bowleven shares since taking charge in 2006. But Mr Kempster asked why he had allowed himself to be diluted following the placing.
"The simple answer is you did not feel that you wanted to commit any more money," said Mr Kempster.
The comment drew a sharp response from Mr Hart, who noted: "There is a limit to how much I can commit. At some point I have to actually feed somebody."
Bowleven's chairman Ronnie Hannah said directors had all shown their commitment over time. He said not all had the resources to maintain their holdings through the placing.
The company faced questioning over its executive pay policies from another shareholder, Sheldon Robins, who said the paper value of the shares he and his wife held had fallen by £150,000 in two years.
Mr Robins asked whether the long-term incentive programme operated by Bowleven properly aligned the interests of directors and shareholders.
Mr Hart said Bowleven had to incentivise management.
He noted shares that vested under a long term incentive programme last December had been deferred until the company reached a final investment decision (FID) to proceed with its plan to bring fields off Cameroon into production.
The FID has been delayed to next year.
Another shareholder asked about the work of Chief Tabetando, a Cameroon-based lawyer who has been on Bowleven's board since 2001.
"For £6000 a week, what does the chairman of Euroil do?" asked the investor regarding Chief Tabetando.
Mr Hannah said the chief had been a very good asset to Bowleven and played an important role in helping it maintain links with key players in Cameroon.
Mr Hart pinned much of the blame for Bowleven's disappointing share price performance on some institutional investors cooling on the exploration and production sector.
Reiterating hopes Bowleven will start production off Cameroon in 2016, he said the Etinde project could be worth around $1bn (£615bn) eventually.
Barry Sealey who co-founded the Archangels investment syndicate, backed the management.
He said: "I think the team has done a very good job."
Noting that the oil and gas business is challenging, Mr Sealey added: "People who are risk-averse should not be investing in Bowleven."
Terry Heneaghan, former executive chairman of Bowleven, asked: "When do we turn around and say we can't realise this and pass it on to someone else?"
Mr Hart's reappointment as a director was supported by 93.9% of proxy votes cast at the meeting.
Mr Kempster and Mr Robins voted in favour.
The company's report and accounts was approved by 92.5% of proxy votes cast.
Bowleven shares fetched 386p in January 2011.