if you want to ride I would route as follows - south to the tower, pick up CS1 to embankment, trafalgar square, the mall, hyde park corner. cycle lanes either in the hyde park or on park lane dependig whether you prefer to avoid fumes or pedestrians wandering over the cycle lanes, edgeware road to paddington.
but best bet is probably circle line from liverpool street to paddington as Adamski says, bikes are allowed because it is not a deep line, but obviously rush hour crowds would prevent this.
