Can I apply for the Tibet and Buthan visa staying in Bangladesh?

1. You mean Tibet Travel Permit and Bhutan Visa, right?
2. As to the Tibet Travel Permit, you are required to join a group organized by a travel agency and the travle agency will get the permit for you. It is the only way of getting a Tibet Travel Permit; But you should apply for a China tourist visa first.
3. As to the Bhutan Visa, you can apply at the Bhutan embassy or consulate in Bangladesh. If your time is limited, you can ask for express service or rush service, which will allow you getting the visa in one or two days.