I can only address the issue of your U.S. vehicle. I have no experience with Bangladesh passports or Mexican visa requirements for Bangladesh citizens.
You are not legally required to buy insurance in Mexico, but you would be crazy not to. If you are in an accident without insurance in Mexico, you stand to have your car impounded, and spend at least a night in jail.
See this related question for suggestions on where to buy Mexican car insurance.
Aside from that, to actually enter the country with your vehicle, you will need:
- Proof that you are the owner of the vehicle. The original title, or registration receipt will suffice.
- Your drivers' license
- Your passport
- 2 photocopies of each (If you arrive without photocopies, you can have copies made there, usually for a small fee, or a tip)
When you cross the border, you will need to find the nearest Customs (Aduana) office. It's usually very near the border crossing, but not always immediately obvious. There should be signs (usually in English, too), pointing to Vehicle or Car Permits.
Once there, expect to spend some time in line. Although how much time varies greatly depending on which border crossing you use, and the time of day. If you can cross early in the morning, or on a Sunday, you may be the only one in line. If you cross during a busy time, you may be in line 2-3 hours.
You will be required to present your passport, and fill out a small permit card (assuming you are entering as a tourist), and return to the window where the clerk will give you (typically) 180 days, and hand the permit back to you.
Then you will go to the Banjercito window where you will pay your fees. There is a visa fee, a vehicle importation fee, and the big thing, a temporary vehicle importation deposit, which varies depending on the model year of your vehicle. You can pay these fees in cash or with a credit card.
You will then receive a vehicle permit to stick in your windshield.
At this point, you are free to enter the country (beyond the "free trade zone").
When you leave the country with your vehicle, be sure to return to the Customs office wherever you are leaving, and turn in your vehicle permit to receive the refund on your deposit.