***** A NON-TEACHER'S OPINION *****
I had never thought much about this matter until I read your
I have checked my dictionaries at home and various online dictionaries.
I have some ideas for you to consider.
(1) You wrote an invitation. Probably most "experts" would
suggest that you simply write:
Please join us on Saturday for Bob's birthday party.
Most dictionaries explain that if the sense of your sentence
means "everyone else will do it," then do not use "with."
Many dictionaries give examples similar to:
Won't you please join me in welcoming our distinguished guest.
I join my wife in thanking you for that wonderful gift.
(2) You do use "with" if the sense of your sentence is
"let's work together."
Residents have joined with the police to reduce crime in the area.
I hope you will join with us in the campaign to cure this horrible disease.
I found the Longman Online dictionary to be most helpful in my research.
Thank you again for the question. I learned something today that I
had not known.
Have a nice day.