How can I apply for an EB-5 visa while still on an H-1B?

You can apply inside the U.S. for a green card if your EB-2 is denied or takes longer than expected as long as you are maintaining your H-1B status, or you fall under an exemption to maintaining lawful status such as Section 245(k) of the Immigration and Nationality Act. Even if you have an approved EB-2 petition (filed under Form I-140) or your EB-2 labor certification is pending for more than one year, you can extend your H-1B after your six year maximum period has ended. Whether you wish to continue to be tied to the H-1B while you wait may be a consideration in applying for your EB-5 visa.

Premium process the I-140 to obtain a timely decision, then evaluate whether an EB-5 petition is warranted. Although the EB-2 priority date is not current, applicants born in Bangladesh remain in a relatively favorable position. EB-2 processing may be comparable to or faster than EB-5, and an approved petition can support H-1B extensions beyond the six-year limit.

You can join a regional center's project to start your EB-5 preparation and filing. You can concurrently file I-485 to adjust your status. With I-485, you can file I-765 for EAD allowing you to work while your I-526E and I-485 are pending. You can still work for the same employer with your H-1B until its expiration and immediately your I-485's EAD can step in to let you continue to work.

Yes, definitely possible and done many times. You may have both cases filed simultaneously and with the second filing recapture the older I-140 Priority Date.

Yes it is possible and common for foreign nationals on H-1B visas to apply simultaneously for a green card in the EB-2 and EB-5 categories. Right now Bangladeshi nationals are currently immediately eligible to apply for the green card (the adjustment of status or I-485) concurrently with the I-526 immigrant visa petition based on EB-5 investment in a rural TEA, and the process may be much faster than EB-2.