I don't mean when someone sneezes or when someone's been kind to you, but in other situations.
Like, when someone is enjoying a lot of luck, fortune or doing staggeringly well in something.
Or when someone is wonderful at a task and you admire them at lot. So, you want to get to know them better through talking to them, either directly or via online messaging. However, they are often quite busy and you're hoping they have time for you, but they turn out not to have any. You can say: "(It's a pity, but) bless them."
Besides, is it the same meaning as "wish you good luck"?
Best Answer
A lot of words or phrases move away from the literal meaning and this literal meaning is bleached or ignored but instead the focus is on the function to express a kind of attitude. Some people call this pragmaticalisation; the phrase serves a pragmatic function of expressing an attitude. Out 'good-bye' or bye started life as 'God be with you' - which originally invoked a blessing on the other person. And people typically invoked a blessing when they parted, so it became associated with leave-taking and the literal meaning was forgotten. We can also think about how 'thank you' often functions not to thank someone today.
'Bless you' has also undergone pragmaticalisation. I would say that 'bless you' expresses a degree of fondness for some people who have disappointed you. In my own usage, it is similar to how I might say of say of children, 'They are uncontrollable, bless their hearts.' I would imagine that it started life as an actual blessing (as mentioned by bobtato). You are typically fond of the people you want to bless, but the usage mentioned, the fond attitude is preserved and the actual blessing forgotten.