Hi,
As you've probably figured out by now, nebraska doesn't publish a death index. You can apply for a copy of a death certificate,
http://dhhs.ne.gov/publichealth/Pages/ced_decert.aspx but you have to know the death date and write it in on the form.
Anyway, ... most death dates are determined from a cemetery record or an obituary.
The bad news for Webster Co. is that very few cemeteries are indexed and published online. I checked those few and Bayles isn't listed. I also checked findagrave.com and nebraskagravestones.com and they are listed there either.
You can contact Webster county Historical Museum,
www.redcloudnebraska.com/attractions/webster-county-historic... They have marriage announcements and obituaries. They might have indexes to the cemeteries in the county too. Successful Searching!
PS - Stephen in 1900 was living in Industry, Phelps, NE with his daughter Susan (Brown) and her family. I'll check that county for Stephen's interment too.