The 10-pin AVR ISP connector is similar to the 6-pin, it just has a lot more ground pins. You'll need to make/buy an adapter to convert the connector down to a 6 pin.

Here's an instructable: http://www.instructables.com/id/Programming-adapter-from-10-pin-to-6-pin-for-AVRs/

Or for US $5 you can buy one from eBay: http://www.ebay.com/itm/USBASP-USBISP-AVR-Programmer-USB-10-Pin-Convert-to-Standard-6Pin-Adapter-Board-/180980285082 This also includes another programmer

Amazon Prime: http://www.amazon.com/Adapter-Board-AVRISP-USBASP-STK500/dp/B00FHHYJ7G

Lots of options to get down to 6 pins.

I don't know what bootloader the AVR on the printerboard uses, but Printrbot does have bootloading instructions on their web site. You may be able to discern from that site what bootloader is on your board. Printrbot support also seems to be quite good in my experience, you may be able to just email them asking for instructions on how to load the bootloader back onto the board.

Why do you think the bootloader is corrupt? A well built bootloader is pretty robust.