"I want to invite her to tea."
Translation:Jeg vil be henne på te.
You can use either "invitere" or "be" here. The verb "å be" can be used as to pray, to invite (as in this situation) or to ask (someone to do something specific). "å spørre" can also be translated as "to ask", but in that situation it means more like to ask someone a question about something.
I was actually thinking of German beten 'to pray', although I wonder if that comes from the same root as bitten 'to ask, to request'. I'm not sure about to beg, but I looked up the Wiktionary page for the English verb to bid, which would seem to confirm that to bid, å be, bitten and beten all share the same Proto-Germanic root 'bidjaną (which of course goes back to an earlier Indo-European root word). English to beg seems to come from a different root word, although they could still be related.