There's no ferry across the Menai Strait. There used to be one many years ago, but not now.
You can cross the Menai Bridge either on the carriageway or on the pavement/cyclepath. Cycling is only really allowed on the pavement on one side (west side - left side as going to Anglesey), but people ride on both sides. As Wowbagger says, it's narrow enough to prevent any overtaking at all - you won't be squeezed as the arches are very narrow. The bridge is undergoing maintenance work as it was found to be structurally unsound in the summer. It was closed to motor vehicles Oct-Jan, but is open to under 7.5t vehicles now.
The Britannia Bridge is safe to ride across. Although dual carriageway on the A55, it's single lane each way on the bridge, with little loss of width, so lots of overtaking space.
You can get round in a day of 80 miles, but that will result in either riding main(ish) roads around the coast (reasonably fast, but boring), or missing half the island.