Routefinders do not give measurements "as the crow flies".
The distance as the crow flies would be between 102 and 109 miles depending on the exact location within each city from which the measurements were taken.
Using Google Earth it is possible to measure global distances in centimetres. However, resolution issues often reduce this to metre accuracy.
Postcode districts are also inexact for measurement purposes since they can encompass areas of many square miles.
Using random locations within the postcode districts you have named (Bath BA1 - Charlotte St and Hove BN3 - Poynter Rd) gives a straight line distance of 102.14 miles.