Protecting Pole Beans from Rodents?

After a few years of delicious crops, my purple pole beans have been discovered by, I suspect, both squirrels and tree rats. They finally took to eating the bean leaves too. Now a few years later, I want to try again by planting in a shallow raised box with a 2x2 or bamboo pole structure and 1/4" fine black garden netting over this. I realize metal mesh, "hardware cloth" might be more rodent proof, but it is expensive. How successful is this plan likely to be?

The invasive black and grey squirrels have effectively eliminated the native smaller brown squirrels. They are so aggressive that they are trying to chew into the cedar shingled garage and house, and have on several occasions succeeded. Then recently the raccoons have enlarged the holes for access to a rodent dinner! The exterminator found "rodent parts' left. Now hardware cloth is being screwed into the spaces under the eaves, between the rafter ends. Welcome to the Pacific NW's 'Critter Corner'.