Hey there @SusanMarie -- thanks for your post!
I want to make sure I am clear on something, as I am slightly confused about what you are asking.
Are you saying that your colleague was able to see your personal connected calendar (i.e. Google Calendar or iCloud Calendar) when opening your booking page + booking with you? If so, this is not something that Calendly allows, so in this case, it would be a matter of permissions you have granted to the colleague via that calendar platform. I would suggest looking at those permissions ASAP if this is the case.
If that is not the case, are you referring to the fact that when your colleague (and presumably any invitee) visits your booking page, they are able to see what dates are available vs. unavailable? If so, this is expected behavior on the booking page.
If what you are referring to is the portion on the right side of the booking page that you see when l logged in that displays when you are available to meet and lists off meetings from your connected calendar, nobody else will be able to see that. The only case in which an invitee would see the same thing/s you see there would be if they had meetings on their connected calendar booked with you, meaning the meetings are the same and as such you both see them.
If I am not hitting the mark in any of these scenarios, please consider posting screenshots and elaborating a bit more regarding this issue. This way, I can take a deeper look and help you figure it out!
Looking forward to hearing back from you!