This sounds like an "ask a cop" issue, but logic says you can leave the golf cart lane and enter the street for a variety of reasons, including left turns and situations when the golf cart (multi-use) lane is obstructed.
Otherwise, when you encounter someone parked in the golf cart lane, as some contractors often do, you would not be able to proceed.
Accordingly, logically, if a bicycle is traveling slower than your cart will go it is obstructing your progress and you should be able to leave the lane to pass it.
I often have other carts pass me when in the cart lane on streets, even when I am at my cart's wide open legal speed of 20 mph. They aren't street legal, just hopped up a bit.
Let us know what the deputy tells you.
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