the amount of discretionary income you decide to use to invest depends on how aggressively you want to buy bitcoin and after investing you can always put what's left from your discretionary income into your emergency funds, this is because an emergency fund isn't a part of your daily, weekly or monthly necessity
It is completely wrong for a person to keep the remaining money in an emergency fund after investing. Because an emergency fund is a necessary fund that should be considered as the last part of a person's basic needs, it is necessary to keep money in an emergency fund before investing from the discretionary income that a person generates after fulfilling his basic needs. Otherwise, if a person goes directly to investing, then there is a risk that his Bitcoin investment will not be long-term because when that investor needs money for an emergency, he may have to sell his Bitcoins to collect the required money. But if your discretionary income is rich enough, then you can invest in Bitcoin after storing money in an emergency fund and later, when a fairly healthy amount of money is accumulated in the emergency fund, you can reduce the supply of money in the emergency fund and start investing aggressively in Bitcoin. For example, if you have just started earning and you do not have an emergency fund and if it is possible to extract your discretionary income from your current income, then if your discretionary income is $ 1000 per month, then you can initially put 20% of your income in the emergency fund. You can invest in other areas including Bitcoin with the remaining money. After a few months of this, when you have a sufficient amount of money in your emergency fund, if you want, you can stop providing money to the emergency fund and later you can invest 100% of your discretionary income in other areas including Bitcoin.
But remember that to make an investment long-term, you need to have a healthy emergency fund, otherwise you may need to sell your invested Bitcoins for an emergency. So just as we need to save for the future (invest in Bitcoin), it is also important to have an emergency fund to make our savings long-term.