Bounce Rate Issue from Phone Button

I'm having an issue on a client's site with a button on their mobile (responsive) site. Client is an emergency service provider and we have had success positioning a phone button at the top of their mobile site. I know all the usual techniques to increase bounce rate, but for this client, the users are not looking to click around. They want to call and they do, which is good and bad. The problem is anytime someone clicks it, which is a lot, it kills our bounce rate.

Does anyone have any ideas how I could still have the single click phone button used, but either direct it to a new page or alert Google through analytics code that this should not be factored into bounce rate?

We tried using javascript onclick, but mobile popup blockers killed that idea. We were hoping we could have the button direct to a new page and give the user a popup to call.

Any help or direction would be very appreciated.

Why is that an issue?

We've tested sites before with different designs. All other factors being equal, a high bounce rate on our sites has lowered the rankings. This effect was more pronounced as you get towards the higher pages 1-3. We've had success staying in higher positions by lowering bounce rates and lack of success when we didn't.

Usually I can figure something out by altering the design, but this is a different business type and I'm stumped how to keep the phone prominent without having an extremely high bounce rate.