If you can't find Bucket (Mac), here are four key things to check:
First, make sure your iPhone and Mac are connected to the same Wi-Fi network. The app's initial setup guide also advises you to check that both devices are connected to the same Wi-Fi.
The iPhone app shouldn't be the only one running. Install the "PicBucket" app from the Mac App Store and have it running on your Mac for your iPhone to detect the signal.
During the setup process, you may have been asked for "Local network access." This permission is required to search for devices (Macs) on the same network. If you denied this permission, you'll need to grant it again in your iPhone settings.
During the initial setup, the app requests "Location access," and the on-screen instructions clearly state that this permission is needed to find Bucket (so Bucket can be found). Ensure this permission is granted.
If you've checked all of the above, try searching again by pressing the 'Scan for Bucket' (or Rescan for Bucket) button on the app's main screen.