Organized rides usually have volunteers positioned at the finish line to jeer and laugh at late finishing riders. JUST KIDDING!!
No one cares how fast or slow you are except you (and maybe competitive friends). Don't ever worry about embarrassing yourself on a ride.
It sounds like you'll do fine if you're already doing 40 miles a week without difficulty. You could probably do 25 miles right now, so in 3 weeks you should cruise through the ride. You'll find too, if there are other riders and a rest stop or two, that you can do a lot more miles than you think.
But you do need to get those bike shorts first.
Kim