Logitech M535 Bluetooth Mouse – Compact Wireless Mouse with 10 Month Battery Life works with any Bluetooth Enabled Computer, Laptop or Tablet running Windows, Mac OS, Chrome or Android, Blue. Restart the Mac Bluetooth Connection on your Mac. Navigate to the Bluetooth preference pane in System Preferences: Go to Apple Menu System Preferences Bluetooth; Click Turn Bluetooth Off. Wait a few seconds, and then click Turn Bluetooth On. Check to see if the Logitech Bluetooth device is working. If not, go to the next steps. I'm trying to add a Bluetooth mouse to my Apple Macbook using Win10 on a BootCamp partition.I purchased the Logitech M557 Bluetooth mouse as it seemed to have a great record for robust installation.-Mouse works great on my MacBook laptop with MacOS.Mouse works great on my HP desktop machine loaded with Windows 10.
According their site, the mouse works with 'Bluetooth Smart Ready device'.
Best Logitech Bluetooth Mouse For Mac
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 )
Bluetooth Mouse For Mac Logitech Keyboard Software
I guess your only option is use of USB hub if you don't have available USB port,