Hi @ChristianWells and @Bud
Our bug pages are searchable by Google and other search engines.
I think the issue that makes searching on Google inconsistent is that bugs are taken offline briefly for editing and then returned to the support site. After that we have to wait for Google to crawl through the support site again to update their search results.
The bugs are available through the support site search more quickly because our search tool indexes our own content more often than Google indexes our content.
We have tried to minimize the types of edits that cause bugs to be temporarily removed, but there still are some edits that trigger a copy review before they can be returned to the support site. We copy review the bugs so that no public field contains customer information or internal only information.
I don't think it is a matter of formatting the search query, using the bug id and "Esri" or "Esri support" should work fine.