Words with "bi-" prefix that no longer mean "two"

billion comes from bi- + million, as it originally meant the product of two millions - in other words, a million million. This usage persists in Europe (see long scale), but in America a billion means a thousand million. (In the long scale this would be called a milliard.)

See https://www.etymonline.com/word/billion

One is biscuit / biscotti, which literally means "twice cooked". Although the prefix here is "bis", it does start with "bi", so...

from Oxford Living Dictionary:

Origin

Middle English: from Old French bescuit, based on Latin bis ‘twice’ + coctus, past participle of coquere ‘to cook’ (so named because originally biscuits were cooked in a twofold process: first baked and then dried out in a slow oven so that they would keep).

The example given by the OP isn't too far off the mark. Rather than bicycle consider the shortened version "bike" where it may be used as part of another word e.g. quad-bike. In this case it is being used to describe a 4 wheeled cycle.