Get-CimInstance -ClassName Win32_BIOS -ComputerName myComputerName
To see all available retrievable properties use...
Get-CimInstance -ClassName Win32_BIOS | Get-Member
Get-CimInstance -ClassName Win32_BIOS -Property SerialNumber -ComputerName myComputerName | Select-Object -Property SerialNumber
To return the same thing without headers, you can use...
(Get-CimInstance -ClassName Win32_BIOS -Property SerialNumber -ComputerName myComputerName).SerialNumber