A truely untested tip - But might work. At your own risk:
The bsdesign file is actually a zip file, containing a large JSON file, so by renaming the file [my-awesome-site.bsdesign] to [my-awesome-design.bsdesign.zip] and unpacking into a folder - Will give you another file named [my-awesome-design.bsdesign]. Rename this file to [my-awesome-design.bsdesign.json].
You can now open this file in Notepad++ (or any other editor you prefer).
Do your search and replace.
Save file
Remove .json extension
Zip file again
Open file in bootstrap studio - and verify changes have been made.
And again - I have not tested this, only thought about it.