Found Birthmother and Siblings

Hi! So over Christmas break I found my birthmother on Facebook. She doesn't post a lot but is very active by liking a lot of people's pictures and she comments a lot. My sisters, an aunt, uncle, and another family member are also very active and actually post things that my mother likes and comments on. I really want to try to get in contact with my birthmother but I'm not sure if she knows about the 'Other' folder. She does have a public page for a small cake making business she runs by herself so I was thinking about trying to send a message through that page. Not sure if that's weird or not... :P Also, since it's over Facebook I didn't want the message to be too long or detailed. I know it's her, but it was recommended that I try to go along the lines of "Is it you?" (not exactly like that). This way she won't feel cornered if I were to say "I know you are my birthmother" or something. My adoptive parents said that they kept in contact for five years through our agency (which went bankrupt and closed recently). When they told the agency to tell her to stop contacting them and sending them things, she kept sending letters anyway. They got her to stop but now that I'm an adult, they are supportive and allowing me to reach out to my birthfamily. As far as the message, I was going to include my name, birthdate, and where I was born. I know there's more I would like to put but those are just the basics. I thought I'd ask about going through her public page. I've read and seen the comments on other posts about the Other folder and how a message that can just sit there. Any thoughts or advice would be appreciated!