"bike" is ambiguous and more often is used for motorbikes rather than for bicycles.
In UK Highway Code it's "cycle track/lane":
https://www.gov.uk/guidance/the-highway-code/rules-for-cyclists-59-to-82

Sorry, honey, I don't know when you were last stateside, or in the UK for that matter, but here there is no ambiguity - a "bike lane" is for bicycles. And I disagree with your sweeping statement/restriction - "bike" is more often used for bicycles.

http://thebikelane.com