Q. Do you recommend programs like Zotero or Endnote for saving/storing article citations and automatically generating Bluebook citations??

Citation Management: 

Please see this FAQ from the Harvard Library comparing citation tools and research managers  compiled by the Harvard Library for tools to organize your research. 

Generating Bluebook Citations

There is currently no tool that will produce 100% correct Bluebook citations. The following tools will produce citations that are close, but are not perfect. You should always double check the content, format, abbreviations and style of generated citations to make sure they are Bluebooked correctly. 

• Zotero has an option for generating Bluebook-style citations. 
• PowerNotes  also has an option for generating Bluebook-style citations.  
• HeinOnline PDF downloads include a Bluebook-style citation on the first page of the PDF.  
• Lexis and Westlaw show citations for every case. 

However, none of these will produce completely correct citation. No automated process will do a better Bluebook citation than a human being reading and applying the rules.