Under the National Labor Relations Act of 1935, pretty much all private employees in the United States have the "right" to hold a vote where if half of the employees accept union representation, the employer must negotiate with the union on behalf of all of the employees. In a non-right-to-work state they can also force all employees to pay dues. That is to say that the "right" to collective bargaining is the "right" to prevent an employer and an employee from entering into a private contract (and in some cases the "right" to force an employee to pay for representation they don't want). Or, to put this another way, one of the great examples of the need for unions, the United Mine Workers strikes of the late nineteenth century, was orchestrated by people who did not have collective bargaining rights. The striking mine workers each decided strike, there was no law preventing the mines from hiring someone else if they could find someone.
Additionally, what is being proposed in Wisconsin isn't removing collective bargaining rights from public employees (a step that Walker could legally take if he wanted to). Half of the teachers could still force the other half to accept union contracts, but they couldn't force them to pay dues and they would have to vote to recertify (keep the union as their representative) every year.
