That's where I usually depart from bound for West End. A S-SW wind
is ideal, but doesn't happen that often, especially in June, and when it does a strong NW wind usually isn't far behind.
What I make sure to avoid is anything much over 15 knots from the SE through East or anything over 10 knots from any northerly direction.
Much depends on your time frame and your attitude about waiting for ideal conditions or going sooner in something a bit bumpier, though a strong northerly goes well beyond a bit bumpy and should be avoided at all costs, but that's more common in winter than in June.
If the winds are blowing consistently out of the SE, a night crossing may allow some lighter conditions.
I like to check a couple online forecasts as well as the VHF
Love Green Turtle. Kept my boat there for a while.