The shortage of banking services has been a major obstacle to the industry, often forcing businesses to conduct sales and pay vendors and taxes in cash, sometimes in vast amounts that can become targets for criminals.
The number of financial institutions working with marijuana companies has been growing, but it's still a small fraction overall.
The Mountain West Credit Union Association and the Maine Credit Union League said in a joint statement that the legislation would "provide the certainty we need ... to service this growing industry."
The measure, which faces an uncertain future in Congress, does not legalize marijuana nationally. But it takes steps to allow banks to handle marijuana funds without the risk of federal prosecution.
For example, it says money from marijuana businesses in states where the drug is legal would no longer be considered illegal proceeds, and it would allow banks to accept those funds without breaking money-laundering laws.
Even then, risk remains as banks face a range of compliance rules by accepting marijuana-linked money. The Bank Secrecy Act requires that banks know their customers well enough to ensure they are not engaging in money laundering, said Julie A. Hill, a professor at the University of Alabama School of Law.
"This likely means that a bank accepting marijuana money would have to do enough research to know that their customers are complying with state law regarding the sale of marijuana," Hill said. "The bank would likely have to confirm that the marijuana is not sold to minors or sold for transport to states where it is illegal."
Banks could face penalties if they don't meet such requirements.
They also are urged to watch for warning signs of possible illegal activity, such as financial statements provided by a business not squaring with account activity.
Because the cost of doing such research would be high, some banks might choose to stay away from marijuana money, Hill said in an email.
If the legislation passes, it's likely marijuana will stay illegal in some conservative-leaning states, such as South Dakota and Kansas. Some banks in those states might then be uneasy about handling marijuana dollars coming from places where the drug is legal.
"I don't imagine the ... financial institution would take that risk to take in funds from a business considered illegal in that state," said Beth Mills of the Western Bankers Association.
Another uncertainty that could give banks pause: The conflict between Trump, who signaled his support for the legislation, and his own Justice Department.
Attorney General Jeff Sessions staunchly opposes marijuana and lifted an Obama administration policy in order to allow federal prosecutors to more aggressively pursue cases in states that have legalized marijuana.
Colorado tried to set up a credit union in 2015 to serve the pot industry but the Federal Reserve blocked it. In Oregon, the state Department of Revenue built a fortress-like office for dropping off and counting cash.
Some pot businesses have tried to open bank accounts by setting up management companies or nonprofit organizations with ambiguous names — basically, by misleading the banks. But those accounts can be shut down if a bank realizes where the money is coming from.
Other proposals in Congress also are intended to open the way for more banks to handle marijuana dollars, but it's not clear if any have enough support to reach Trump's desk.