Honestly, being called "man" barely raises any alarms, and dude doesn't raise them at all. Hell, I "dude" my female friends all the time. It's definitely not the same for everyone. The mom of one of my best friends knew me long before I was out as trans or transitioned, and even though she's doesn't mess up pronouns with me ever, she'll call me dude, then immediately correct it to "girl".
I don't know if she's worried that she'll offend me, or if she is correcting herself because she doesn't call other women "dude", but I only even notice because she's constantly correcting herself.
That said, you did good by apologizing to her.