Of course it was going into Bluefield's "general budget." The City owned it and operated it as a General Fund activity.
From the 2016-2017 audit, the City of Bluefield received line item revenues of $332,350 for "Rents, Royalties, and Concessions," $506,773 listed as "Contributions from Other Entities," and $655,490 designated as "Parks and Recreation." Impossible to tell exactly which revenues were tied to the stadium, but a quick overview suggests these as likely sources related to the operation.
Compared with $1,815,320 in expenditures for "Parks and Recreation" it appears that the facility was not generating nearly enough revenue to cover its operating, capital, and/or maintenance expenses, the schools and colleges weren't contributing enough to offset those costs, and the taxpayers of Bluefield were making up the difference.
I'd like to be able to dig deeper into the line items themselves, but it appears that the City Manager made a good recommendation in terms of pure business analysis.
Financial information for WV cities can be viewed online at https://www.wvsao.gov/LocalGovernment/Default