The closest place I can find, which definitely does B&B, is 1.5miles from the ferry:
http://www.crescentparkhouse.co.uk/
However, the Ayrshire & Arran Tourist Board might be able to suggest something closer:
http://www.north-ayrshire.gov.uk/na/wlinks.nsf /index/C7CFE6650407B19B80256F0800545104?OpenDo cument&MenuType=Leisure%20and%20culture-Touris m%20and%20travel&DocDisplay=NoDoc&DFBC=Accommo dation&CatLevel=2||
Otherwise, I suggest ringing round the pubs in Ardrossan. They might do B&B or know of somewhere local which does. (Pubs often have the details of local B&Bs pinned up by their phone).
These pubs are all within easy walking distance of the ferry:
Harbour Inn, Harbour Street, 01294 465675
Lord Carson's, Princes St, 01294 605565
Character's Bar, Glasgow St, 01294 465910
Castlehill Vaults, Princes Place, 01294 462398
Charlie's Bar, Glasgow St, 01294 465910
These two are a bit further away but you could probably still walk it:
The Red Herring, Young St, 01294 462354
The Tap Shop, Young St, 01294 462354
Chris