Just FYI and an attempt to sway you in favor of https :)
 "Google to prioritize secure websites" article on BBC 
http://www.bbc.co.uk/news/technology-28687513

I understand. The problem is that the php file resides on a secure server. My university only allows cgi on secure servers. 
Both Chrome and Firefox detect this and silently block the content requested over http.
In chrome, there is a shield which appears at the end of the address bar and I can manually choose to display insecure content and then the page loads just fine, but obviously I cannot expect anyone viewing the page to do the same.
Safari seems to work fine though.

Do you think it there can be a work around if I locally host the bibbase.min.js file on the secure server and just provide a relative path in my php file? 
I will try it to see what happens. 

Perfect! Thank you so much Christian.
I want to say that I really think Bibbase is the best utility for listing one's publications online.
I will recommend it to all my colleagues.

Christian, the web services at my university are taking a closer look at the server error logs. 
Meanwhile, can you shed some light on what Bibbase does to fetch the file ? 
As you correctly pointed out, the bibtex file is retrievable via wget. 

Christian,

Thank you for the prompt reply. 
I will run this by the web admin at my end.