The states that prohibit citrus being shipped into the state are commercial citrus growing states. This is to prevent movement of citrus pests and diseases. Latest plague to decimate the citrus industry is Citrus Greening Disease. It is likely Florida will cease to be a citrus growing state due to this disease. California has some areas with this disease, so states like Texas don't want it to spread to their state. Ornamental citrus can carry the diseases that infect the commercial citrus. So meyer lemon trees to Texas is a no no.
You can ship if you have the trees inspected by the USDA - APHIS, plant protection office. Normally a $200 fee per shipment. Commercial nurseries will go through the trouble, not economically feasible for us hobby growers. In addition, plants shipped have to be bare root, free of all evidence of soil. Easy for orchids, not at all easy for most bonsai trees.
FYI - most international airports have a USDA-APHIS office, for me it is Chicago O'Hare Airport. I brought an orchid I was sending to Nepal to get the Inspection certificate. They were actually quite helpful, but it is a cumbersome process. Plant made it to Kathmandu in good shape. I was actually sending an orchid to Nepal that the parent material was native to Nepal. It was a species that had been over-collected in the late 19th century and now was so rare that many thought it had gone extinct in Nepal. It is actually common in the orchid hobby, raised by seed from plants collect 100+ years ago. So Paph charlesworthii is now back in Kathmandu.