GenomeBrowse does not currently have batch script capabilities directly, so the only way to load a large number of files automatically is through the process of using the IGV functionality as you have described.
GenomeBrowse does have that ability to drag and drop files into the plotting window. So another option would be to open a file explorer to the location of all of your BAM files and then drag and drop the ones you would like to visualize directly into the plot window.
Depending on the size of the files you may want to use our command line program "gautil" to first compute index and coverage for the files so these computation does not overwhelm your system. See our manual for further details.
Let me know if you have any further questions.