Dear Ms. Weidlein,
Thank you for posting your request on History Hub!
The American Railway: Its Construction, Development, Management, and Appliances, by Thomas Curtis Clarke, published 1889, discusses the role of bridge supervisor (aka supervisors of bridge) on pages 154 through 155. While not specific to the Burlington Railroad, it is likely that practices were similar throughout the industry.
We searched online and located Burlington Northern Railroad Company Records, 1876-1971 at the Museum of History & Industry, Sophie Frye Bass Library. You may also wish to contact one or more of the many railway museums and railway historical societies for further information.
We hope this is helpful. Best of luck with your research!