The Right Bike for This Ride
The G.A.P. trail is hard-packed dirt and gravel, and is well maintained.
Taking a Road Bike on the Trail
A road bike is absolutely fine too, but you will need to stop by your local bike shop and temporarily install some wider tires. Look on the side of your road bike tires and you'll see the size, which probably looks something like this:
It's that "23" number we care about. It describes how fat the tire is. The larger this second number, the fatter the tire.
(Hybrid and mountain bike tires are sized differently -- no need to head down that rabbit hole right now! If you are riding a hybrid or a mountain bike your tires are already the right size for this ride.)
The tires that came on your road bike are typically 700x23 or the slightly fatter 700x25, and they get bigger from there. For this trail, don't ride on anything skinnier than 700x28, and even tires as wide as 700x36 would be nice if they fit your bike.
You don't want to wait until the day before the ride to do this -- not all tires fit all bikes. (For example, my own road bike will not accept a tire any wider than 700x23 -- that particular bike won't work for this trip!)
The issue here is if wider tires will fit without rubbing against the frame or brakes. I would NOT order new tires online; you really want to take your bike with you to your local bike shop for this.
If you are traveling with kids the tires that come on a Burley trailer or tag-a-long will be fine on this trail.
SO... what sort of bike should you ride for this trip? Your choice!
Any hybrid around-town bike is great, and the tires that are on it are fine (assuming they are in good shape).
If you have a mountain bike that's good too. (You can ride giant knobby mountain bike tires if you wish, but they are not necessary).