In this case, 'to being' would be correct! You are right that 'to' usually follows 'used!'
If there is an 'am' in the sentence (i.e., 'I AM used to being on my own.') then you say 'used to being.' In this case, it implies that you habitually partook in a certain action and no longer do it.
However, you can say 'used to be' sometimes too, but it depends on the phrase. For example, 'I used to be an astronaut' would be correct since the 'am' is omitted. When saying 'I used to be,' it implies that you were something, and now you are not.
Hope this helps! Good luck :)