If the arrest was recent
Start with the county jail
Someone just arrested in Wyoming and not released is held in a COUNTY JAIL / detention center run by that county's Sheriff, not in a WDOC state prison - so the Wyoming Offender Locator will not show them.
County jail rosters are fragmented: a few Wyoming sheriffs post an online jail roster or booking list, but many do not.
The statewide online path that reaches county-jail custody is Wyoming's VINE system (search at vinelink.com, choose Wyoming), which covers custody status across state prisons AND county jails and lets you register for free phone, email, or TTY alerts when status changes; Wyoming victim services/VINE is administered through the state (Wyoming Board of Parole victim services and WDOC victim services).
For a very recent booking or the bond amount, call the county sheriff's detention center directly.
County jails are run by the 23 county sheriffs; only some publish an online jail roster. Use Wyoming VINE (vinelink.com, select Wyoming) for county-jail custody status - Wyoming VINE covers both state prisons and county jails - or the county sheriff's roster where one exists, and call the county detention center for very recent bookings and bond amounts.