Maybe you can override the partials which display the form.
You copy the needed files (which display the form) from modules/Collecting/view directory to themes/yourTheme/view directory, then you edit them to add specific classes.
I haven’t tried, but I think it is possible.
You can also use other CSS selector (there is not many form tags in a Omeka S site).
However the line only calls the form (<?php echo $this->form($cForm->getForm()); ?>) , it doesn’t add anything like classes, so this must be done somewhere else.
I could just use CSS selectors, but I am creating a theme based on bootstrap, so it would be much easier to just insert the correct classes for the form and each input type.
I don’t know Bootstrap very well, but I believe it is not a good solution for Omeka S theming because you will have the same problem for each view Helper.
However, you can set class attribute with Element::setAttribute() method.