How do I create a new empty file in a bash script?

Use touch command. touch filename.txt.

Use the null command (:) redirect (> filename) trick (:>), as this will truncate to zero or create the named file.

$ echo foo > filea
$ :> filea
$ wc -c filea
       0 filea
$ rm filea
$ :> filea
$ wc -c filea
       0 filea

(This will fail if the shell sets a NOCLOBBER option.)

You could always use perl, too.

$ stat filename.txt
stat: cannot stat 'filename.txt': No such file or directory
$ perl -e 'open($fh,">","filename.txt") or die $!;close($fh)'                                         
$ stat filename.txt                                                                                   
  File: 'filename.txt'
  Size: 0           Blocks: 0          IO Block: 4096   regular empty file
Device: 801h/2049d  Inode: 280728      Links: 1
Access: (0664/-rw-rw-r--)  Uid: ( 1000/ xieerqi)   Gid: ( 1000/ xieerqi)
Access: 2017-02-08 13:51:01.479121995 -0700
Modify: 2017-02-08 13:51:01.479121995 -0700
Change: 2017-02-08 13:51:01.479121995 -0700
 Birth: -