Both sentences are acceptable English, However, they do not have exactly the same meaning. The first sentence, "I was used to living alone", implies that living alone was the current status, had been the status for some time, and was not expected to change. The second sentence, "I have been used to living alone", implies that a change of status has recently occurred or was about to occur ... that is, the person had lived alone for some time but no longer did so or would soon not do so. Both statements are sufficiently abstract that their meanings can be substantially changed by their context.

I think both mean exactly the same thing.

The first is fine. The second doesn't work as written. Depending on meaning: I was used to living alone. I had been used to living alone.

"I have been used to living alone" implies that this has changed, i.e. "but recently my grandchildren moved in with me and life has been much more fun since then." "I am used to living alone" = it's normal for me and doesn't bother me / I accept it.