The original post doesn't mentioned extraction of the Bento data to the iMac, but Filemaker
has very specific instructions for getting this data.
You'll have to create a new sync. When you create a new sync, the data from the iPhone is copied into a Backup folder on the Mac, and the Mac overwrites the data on your iPhone, making it appear the data is lost. Here are the exact steps.
1. Launch Bento for iPhone. Tap the sync icon at the bottom of the display and tap "Sync with a New Computer". A passcode will then be displayed.
2. Launch Bento for Mac. Pull down the File menu and select "Set Up Sync with Device...". Your iPhone should then be listed and highlighted (if not, then the Mac and iPhone are not on the same Wi-Fi network). Click "Continue...", and enter the four-digit passcode that is displayed on the iPhone from the previous step. The Mac will then start the syncing process by copying the database from the iPhone to a Backup folder on the Mac, and then moving the database file from the Mac onto the iPhone.
3. When finished, quit Bento for Mac.
4. Go to where your bento.bentodb file is located. That is,
[User Account] -> Libary -> Application Support -> Bento -> bento.bentodb
(If you have trouble finding your personal library folder, click the "Go" menu in the Finder, hold down the Option key and click Library.)
5. Rename "bento.bentodb" to "mac.bentodb". This saves your Mac database.
6. In the same folder as mac.bentodb, you should now see a Backup folder preceded by the name of your iPhone. For example, "David's iPhone Backup". Open that folder, and if there is more than one file (which means you have tried this before), find the most recent file and rename it bento.bentodb
7. Move the bento.bentodb file up one level (out of the Backup folder) so it resides in the same folder with mac.bentodb
8. Launch Bento for Mac. You will now see the data that existed on your iPhone.
9. Create another new sync in Bento for iPhone to move the data from the Mac to the iPhone.