Hello,
I would like to add image titles above each thumb using bxslider_thumb_nav extension.
I can add the file name using
$imgobj->getFileName();

but using
$imgobj->getImageTitle();
does not work.

getImageTitle() is located at template-functions.php - maybe the reason why this function is not available with bxslider extension.
It's by the way explainded as an example here:
https://www.zenphoto.org/news/zenphotos-object-model-framework/
You can always consult the documentation here:
https://docs.zenphoto.org/1.5.x/class-Image.html
And note about class inheritance of parent classes.