Bangladesh is the beneficiary of US Generalized System of Preferences (GSP) Program (low or no tariff penalty). Bangladeshi products such as golf equipment, sleeping bags, bone china and porcelain kitchen/ tableware, cereal based prepared foods, hand-loomed woven cotton carpets and other textile floor coverings, spectacles and goggles, headgear other than rubber and plastics, etc. are eligible to enter duty-free under GSP in the US market.
There are no additional rules for exporting handmade carpets from Bangladesh to USA. Go forward!
As far as I know there are no such restrictions. But your production must be done under the control and must have certifications: certificate of origin, inspection certificate, product testing certificate, health certificate, phytosanitary certificate and/or fumigation certificate if required. Good luck!