Logitech unifying receiver: Connect up to six Unifying compatible devices with one tiny wireless receiver that stays in your laptop. Logitech's most advanced wireless trackball for Windows PC and Mac requires 20% less muscular strain than a regular computer mouse.

According their site, the mouse works with 'Bluetooth Smart Ready device'.

Logitech Bluetooth Trackball Mouse

http://www.logitech.com/en-us/product/mx-anywhere2 ( Check System Requirements in TECHNICAL SPECIFICATIONS section )

Bluetooth Smart Ready on Mac means Bluetooth 4.0 hardware with Yosemite or later.

Unfortunately BT on your Macbook Pro (mid 2010) is BT2.1+EDR

( If you want to be sure, Logitech provides a procedure to check the PC/Mac is Bluetooth Smart Ready or not )

Logitech Bluetooth Trackball Mac Software Windows 7

I guess your only option is use of USB hub if you don't have available USB port,