I've taken the ferry from Italy to Greece (and back!) several times and did it the cheap way, ie. no cabin, just kipping in a quiet corner on deck somewhere. As such, I'd recommend you keep your doss bag with you - the crossings I took were overnight, and they aren't like a little hop across the Channel, all fruit machines, spot of lunch in the cafe and then you are there. No, I seem to recall that the crossing from Ancona to Patras was about 20 hours, and from Bari about 15 hours. Even Ancona to Igoumenitsa is a good 5 hours.
The boats I took were teeming with, um, those "nice exotic itinerant folk" that Nigel Farage keeps warning are going to launch an invasion of Blighty, and they all apparently wanted to be friends and mill around me, so I've been glad to get inside the bag, fully clothed, with my tankbag as a pillow, and all my valuables upon my person, out of the way. Maybe next time I'll get a cabin, just because I'm getting too old to be slobbing about in all my sweaty riding gear for days on end, and it'd be good to be able to lock the door behind me and relax without worrying about the smiley chap who is invading my personal space while his mate stands directly behind me. Jeeez, I hate that!
The vehicle decks are secure while the boat is at sea, and they are strict about that, so your bike (and anything strapped to it) will be safe, although I think they allow people with campervans access to their vehicles on one dedicated "Camp + Sail" deck, so perhaps watch out if you end up on the same deck. I left my lid locked to the bike with no problems.
As far as I'm aware, the ferries across to Greece don't put out if the weather is anything more than a bit blowy, certainly nothing like North Sea or Channel crossings routinely are, pitching and rolling, but the crews know what they are doing when it comes to securing your bike.
Out in the Greek Islands they use ex-North Sea boats, and they don't sail if there's any white tops at all! (Just as well, because they just put a bit of baling twine on one handgrip and tie it to the side of the boat, no messing about with seat straps!!)