Monday was probably chosen as the best day because many people worked a 6-day week, with only Sunday off. Giving them Monday off as well extended their break from one day to two.
Many sources suggest that Sir John Lubbock's love of cricket was involved in him proposing the introduction of Bank Holidays to Parliament; he wanted more time for people to be able to play and watch the game.
It's also worth noting that bank employees weren't particularly short of holidays themselves. The four Bank Holidays replaced the 33 saints' days and religious festivals upon which the Bank of England had previously closed. The Bank Holidays Act 1871 simply stated that there could be no obligation upon anyone to complete a financial transaction on a Bank Holiday and that where, for example, a payment became due on a Bank Holiday, it would be regarded as having being settled on the due date if the payment was actually made on the following day.
https://www.ancestry.co.uk/contextux/historicalinsights/bank-holiday-act-1871