We have an open-door invitation here regarding friends.
I would invite both-and let them know you have invited both.
They aren't required to appear just because you extended an invititation.
Be yourself-issue both invites and give them the respect and grace to make their own decisions regarding their comfort level and interest in attending.
I find it ANNOYING when people micromanage my time. It would bug me to have a boyfriend or potential boyfriend who thought he could decide whether or not I should/shouldn't be invited "for my comfort". Shy, outgoing, nervous, whatever-it's MY choice if I want to go or not.
I would expect someone interested in me to respect me as an adult who is fully capable of deciding-by giving me the invite and the pertinent info.
"Love As Thou Wilt"