Can we give vendors access to BQE CORE?

You can allow your vendors to use BQE CORE by creating vendor records of type Contract Employee for them in the Create Vendor dialog. You need to set up their account and user profile, just like you do for any other user (employee). Check CORE Help for details.  You also need to purchase a subscription for the vendors and assign it to them. 

You can easily create vendor bills from the vendors' time and expense entries. Check CORE Help Center for details on that.