Method 1
Audio Files from Regions
Save the project including the audio files under another name. Select all regions of your track. From the Arrange menu, choose
Audio -> Convert Regions to New Audio Files
This is the quickest method and the only batch processing I know. You find the new files in the audio folder of the project and in the Media Bin. You can set a name and Logic numbers the files sequentially. From the Media Bin you can save the files with other names. Or just move and rename them in the Finder.
With this technique each generated file is as long as the original region. You cannot use it if you have reverbs or delays in the track because the audio tails would be cut off. In this case you may first bounce the regions in place and cut them or use another method.
Method 2
Track Export
This method handles audio tails without bouncing in place and cutting afterwards.
Save the project including the audio files under another name. Create as many audio tracks "with duplicate settings" as you have regions, this will copy your plugins to each track. Move each region to a track. Delete all tracks you do not need because every track with a region will get bounced, regardless if it is muted or hidden. Set the song end after the longest region, leave enough space for audio tails. Then select
File -> Export -> All Tracks as Audio Files
The length of the bounced files is not predictable and you cannot export with custom filenames. Your bounced files will be named like the tracks plus the extension _bip.
(file format)
Method 3
Individual bounces
Select the first region and use the KeyCommand
Set Locators by Regions (default: ctrl=) which generates a cycle range in the timeline that is exactly as long as the selected region. Bounce this region as usual. You can set your own filename and the lenght of the bounced file will be as long as the cycle range. Do the same with all regions.
If you do not want the file length like the region length you have to adjust the cycle range manually. Of course you have to do this if you need audio tails.
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If you want all bounced files with the same length and set your own filenames, you can either use method 2 and bounce each track individually or place each region at a bar and use method 3 with a manual cycle range. You can drag the range from one region to the next for each individual bounce.