As stated above, plan your trip with Eldridges current table. DO not try passage through Plum Gut against the tide, you won't make it, period.
Leave Bridgeport on an early morning ebb and get as far as you can down the coast of CT. Plenty of places to overnight along the coast of CT. To be honest, on a 22ft boat, I would plan three days.
Depending on the wind, current and how many hours you care to be a slave to the tiller. You could definately make it in two, but three might be more fun and relaxing.
Plan your passage through the Race or Plum Gut just before the Ebb ends or slack, but, you MUST get through before the start of the flood. If you make it around the N. fork of LI too soon on the Ebb you will have the tide against you as you head West towards Shelter Island. The flood will take you in towards shelter Island faster.
If the weather is anything less than very favorable you might want to avoid Plum Gut and go through the race.
Don't underestimate the pounding you can take through the Gut or the Race, even with a fair tide. Don't get me wrong it's loads of fun as long as you are prepared for it. Eldridges is your best friend. DO NOT plan your trip with the tide! Use the current table! (sorry if I'm overstating this, but, some people are not aware that the tide/current are not on the same schedule and as much as 2-3 hrs different).
Sounds like a great trip and this is a great time of year to do it. I wish I was going with you