In order to better understand what might be the issue here can you please share the following information?
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Is this happening with a particular project or is it happening with several projects?
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Do you have edit rights on the Project you are trying to add? (You can confirm this by clicking on the Share button next to the Project name).
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Would you mind sharing a screenshot of the search result when you are trying to add the this project to the Portfolio?
Regarding the option to bulk add projects to a portfolio, this is not possible yet but there is an existing thread in the #productfeedback category suggesting this feature. I would suggest you to upvote it here: Add multiple Projects to Portfolio at once - #3 by Marie
Looking forward to your reply Brandon!