If taking your own bike (Apart from flying it there), the only way is the ferry from Denmark.
We did it in August. Ride from the UK to Denmark (Aalborg), caught the ferry and arrived in Iceland a couple of days later. Great fun, can't recommend Iceland enough!
Smyril Line - Travel to Iceland and Faroe Islands by Ferry is the only ferry company. Book well in advance as it fills up and become pretty expensive. Think I paid €800 for a trip "off peak" in the couchette accommodation.
If you have the time available they often have specials where bikes can travel free as long as you spend a few days in the Faroe Islands although I can't see any of those on the website at the moment.
Here's my little write up from earlier this year if you're interested.
Iceland | Elige
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