Your profile photo, first name and last name as well as your approximate position are always public for every registered and authenticated (except blocked) BIZZDAR user in the app. As these are the basic components allowing the functionality of the BIZZDAR mobile app, you can hide your full profile by deactivating your profile (no need to delete your account) by clicking on the "Deactivate account" toggle in your profile settings.
But you have two other options:
A) Profile Info
When editing your profile (Edit button on your profile) you can simply use the toggles to show or hide certain entries and profile information. A switched on toggle means, that your information is publicly visible. To hide certain info, switch off the respective toggle.
B) Location Checkin
You can also use the toggle on the location checkin page to hide or show your location that you checked in at.
Please note that this does not affect your profile's approximate position within the BIZZDAR grid or list view. Other users can still estimate their approximate distance to you and your current position.