It is the early days of bitcoin that we should be very much cautious about the advice of investing what you can lose into bitcoin. We can take such advice seriously for shits but for bitcoin, invest the amount you want to use for investment. If you have $10k and you want to invest $3k, invest it, even if you can't to lose it.
Your money is not going to loselt in bitcoin and we all know about it. So, what is the essence of investing only what you are able to lose?
If $3k isn't your discretionary income and you invest it into bitcoin, you will end up selling it when the need for that money arises. You don't invest with any amount of money into bitcoin without proper calculation to know if that money is your extra cash that you can do without in the long run.
Bitcoin investment is not guaranteed to be profitable in future and that's the main reason why you should invest with your discretionary income. It's called the amount of money that you can afford to lose because whatever you use the money for, it wouldn't affect you financially.