Tellico uses the bibtex property to know how to export bibtex fields. If you want to add additional fields to export, such as an abstract, open up the Collection Fields dialog, and click the Set Properties button. Add a bibtex property with value abstract. Then, when you export to bibtex or bibtexml, that property will be used for the bibtex field name.

How do I export additional bibtex fields?
How do I export additional bibtex fields?