Thank so much Christian, for your help and patience.  It turns out I was looking at the bib file in BibDesk (Mac) and it was hiding the LaTeX escape codes - so that is taken care of - thanks again.  I have a couple of further questions - if I may ask them here.

1. Must I use the Unicode characters for Bibbase?  I ask because one of the things I really like about it is I can use the same bib file for my publications, CV, and my web page.  But I use latex escape sequences there, mostly.  Do people use only Unicode these days in bib files?
2. In the abstract for the bib entry we've been discussing, the LaTeX (e.g., em dash, single quotes, etc.) doesn't come out as LaTeX'ed.  Is that just the way it is?  Should abstracts not have LaTeX in them?  Again, this might raise the question of #1 above regarding having to keep multiple bib files for web, CV, etc.
3. Is there a way to handle the url in the first (ORBDE Software) entry under 2014 on my page? [Sorry if I should post this question separately.]

I double checked, but that is in fact how it is in the bib file.  (I think you can see this by expanding the 'bibtex' option on the web page.  Could it be the CSS file?  What should that look like?

I am having a similar problem.  See https://academic.mu.edu/peressini/afp_pubs.php.  Two entries under 2019 pubs come up without accents:  "Otavio" and "Scholler".  I've done eveything as suggested (best as I can tell).  I suspect it is in my bib file?  Thanks for any help.