The money from your share sale will normally be sent to your account on the 3rd business day following the day your shares are sold. For example, if your shares are sold on a Monday (Day 0), you can expect the money to be sent to you on the Thursday (Day 3), which means it will likely turn up in your bank account Thursday afternoon, evening or worst case, by Friday morning.
There is no way to speed settlement processes up, it is just a reality of dealing in financial markets.
Why don’t the share and cash transactions just occur at the same time?
One of the functions of the ASX is to act as an intermediary between buyers and sellers, often referred to as a ‘clearing house’. Imagine if after selling your shares the buyer then didn’t pay you the cash, or if you bought some shares and then never received the sellers stock. This is where a clearing house steps in. By handling all the transactions that occurs on the ASX, they are able to effectively eliminate the effects of a buyer or seller defaulting on their obligations by spreading the risk of this occurring across the entire market.
Although the technical process of how this takes place is largely automated, still takes a few days and an office of support staff to complete, which is why transactions take a few days to settle.