Bashar announced his decision to step down on Sunday after his team lost a Test series 1-0 to India following a 2-0 one-day series defeat by the visitors.
The 34-year-old batsman said his continued captaincy of the Test squad depended on the Bangladesh Cricket Board, which might soon decide on his future in the Test squad.
"I have made up my mind. I don't want to be the captain of the one-day side any more," he told reporters after Bangladesh lost the second and final Test by an innings and 239 runs.
"However, I'll be available before the selectors for the one-day squad. If they want me in the squad, I will definitely play."
Bashar led Bangladesh to 29 one-day victories in 69 matches, but came under fire after making only 105 runs in the World Cup.
His duck and 43 runs in the two one-day matches against India in the just-concluded series did little to help to his cause. A third match was rained out.
Bashar has led Bangladesh in 18 Tests with one win, 12 defeats and five draws but he has come under scrutiny after making just 46 runs in four innings against India.