"It's tough, no doubt, but not impossible," Bashar told reporters on the eve of his team's departure for the Caribbean for next month's tournament.
Bangladesh are in Group B with former champions India and Sri Lanka, and debutantes Bermuda, with the top two sides advancing to the next round.
"Both India and Sri Lanka are very good teams. They are going there to win the World Cup. But we are confident we can beat either of these sides to book a place in the second round. It's our goal," said Bashar, 34.
He said a string of victories in recent years -- including against defending champions Australia, as well as India and Sri Lanka -- had boosted the team's morale.
"We have been beating big teams. Previously, when we beat a big side, it was unexpected. But not now. We are now a matured side going into the World Cup with a lot of victories," he said on Sunday.
Bashar said his team also hoped to erase bitter memories of the last World Cup when they lost all of their matches, including against non-Test-playing nation Canada.
Bangladesh have won just two of their 11 matches since making their Cup debut in 1999 in England.
"We want to forget those bitter memories. I am sure we will do better than the last two World Cups," Bashar said.
Bangladesh coach Dav Whatmore said his team's target to reach the second round was now more "realistic", but cautioned the team had to think "out of box" to beat India or Sri Lanka.
"We have to think out of the box ... we have to come up with a particular plan to catch someone unawares," he said.
Bangladesh vice captain Shahriar Nafees said the team had learned how to beat big sides.
"Since 2005 we have been beating better sides, like Australia, India and Sri Lanka. We've learned how to beat a big side," he said.