The bill addresses these concerns in two ways.
First the Speakers, as custodians of the parliamentary privilege, are in charge of the service. They also have the power to issue broad policy direction. In addition to all of that, there is another provision that says nothing in this bill affects the privileges of the House and the Senate. Essentially this means that every recourse that exists now, including bringing matters onto the floor of either the Senate or the House, will be preserved and will exist.
The other item that I think is important is that this new person who will be charge of the services will be selected in collaboration and in consultation with both Speakers. So the Speakers will select this person with the RCMP through a transparent and consultative process.