You must say "get used to being alone." - this means that people who are a little bit strange become accustomed to being alone 他们习惯了. Example: "Some people can't ever get used to being alone." "Used to be alone" means that something has changed. 改变了. In the past she was alone, but now she isn't. "She used to be alone, but now her friends are here." Also, the sentence you wrote needs a comma: When you're different, when you're special, sometimes you have to get used to being alone.

Although I don't completely understand your Chinese, that sentence is for sure "getting used to being alone", because you are adjusting to a condition that will persist (continuous). "to be alone" suggests temporarily being alone. But if you are going to get used to it, then that means it is not a temporary condition, otherwise you would not need to get used to it.

I guess get used to being alone is correct.