Discretionary income has become too generic here, and if you investigate the lives of those who really make it through Bitcoin and the majority of those who keep investing in it despite being expensive, you would realise that it's not about discretionary money, but a determined mind. Fine, using discretionary money to invest in Bitcoin is cool and safer from worries, but risk-taking is beyond that, and people still take risk painstakingly for the later gain. They adjust lifestyles, delay some personal/immediate gains, sort for money elsewhere, just to invest, etc. Some are now millionaires for taking the risk, while some have remained where they were because they always couldn't save reasonably in the name of discretionary income, let alone have enough to invest in Bitcoin.
I don't think that a brand new investor needs to wait until he has enough discretionary income before he can start his bitcoin investment because waiting till you have enough discretionary income can lead to delay to kick-start your bitcoin investment since the amount of discretionary income that you call enough might be very little to the other person.
If your discretionary income is as low as $10 or more, you can start your bitcoin investment right away. Consistency is what really matter when using DCA method, because it's only through consistency that a drop of water can turn into an ocean. Having a long-term investment mindset and a bitcoin target to accumulate will help you stay focused.