There is no evidence to suggest that owners have anything to do with it at all. The burms are breeding in the Everglades on their own. They will continue to do so, regardless of whether anyone in the country owns burms.
People are not releasing them--or, if any are, they aren't having any impact on the numbers in the Everglades--so even stopping people from owning them will not help this issue.

Capturing the burms in the Everglades is going to be the only way to get rid of them, but it's not an easy task. My personal opinion is that they should just open season on them--make people take a short quiz on identifying Burms as opposed to other snake species, and then give them a license and let them have at it. Burms are a lot less dangerous than bears, and no special knowledge is required by the government to hunt those, apart from basic gun safety.

It's going to take time, and it may not work anyhow. Once a species is established in a wilderness area, it's not that easy to eliminate. Burmese are fairly secretive and cryptically colored animals. The idea of finding all of them in a giant swamp is rather ludicrous.

This bill is irrelevant to the problem of Burms in the Everglades. Resolving that problem requires hunting, and nothing more.