Storing a mountain bike and surf boards, and still having enough room to make an ocean passage with a few people in comfort... not gonna happen on your budget. Even with a folding bike, the bike and surfboards are going to wipe out a cabin in terms of space taken up.
The only way you might make this happen on your budget is to get a smaller catamaran, like an Iroquois, Catalac 8/9M or something of that sort. They'll have the space for stowing your bike and surfboards, as well as be large enough to carry a few people across the ocean... and have a small party on deck. No monohull you could afford is going to do it, or be in the shape to do it without a fairly massive investment in refitting, repairing and upgrading.
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You know what the first rule of sailing is? ...Love. You can learn all the math in the 'verse, but you take
a boat to the sea you don't love, she'll shake you off just as sure as the turning of the worlds. Love keeps
her going when she oughta fall down, tells you she's hurting 'fore she keens. Makes her a home.
—Cpt. Mal Reynolds, Serenity (edited)
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Still—DON'T READ THAT POST AGAIN.