It is as simple as just following the relevant bridge account, and your posts will appear on the other side with the same address you are currently using. So you are not creating a new profile on the destination network. The profile name is not identical to the one you currently use, as I see “ap.brid.gy” is appended, but the name is easily searched for and found.
Once you’ve determined what your profile’s account name is on the destination network, you can share that with any friends there, who will be able to follow it and interact with you. Unfortunately, if you have an actual account already on the destination network, you can’t yet bridge with that account. And, of course, some admins may choose to block the bridge.
But, as is the custom on the Fediverse and Bluesky, you won’t see these bridged accounts unless you decide to follow them. There is no algorithm pushing or promoting such feeds into your feed. It is your choice.
See https://lifehacker.com/tech/bridgy-fed-connect-mastodon-and-bluesky