.....I got it.
Public Function GetBoundingCoords(ByVal Filepath As String, ByVal Filename As String) As IGeoDataset
Dim coordXMax As Double
Dim coordYMax As Double
Dim coordXMin As Double
Dim coordYMin As Double
'***** Option 1: *****
ESRI.ArcGIS.RuntimeManager.Bind(ProductCode.EngineOrDesktop)
'Instantiate engine component.
Dim doc As IDocument = New ESRI.ArcGIS.ArcMapUI.MxDocument()
Dim wFactory As WorkspaceFactory = New RasterWorkspaceFactory()
Dim rWorkspace As ESRI.ArcGIS.DataSourcesRaster.IRasterWorkspace = CType(wFactory.OpenFromFile(Filepath, 0), ESRI.ArcGIS.DataSourcesRaster.IRasterWorkspace)
Dim rDataset As IRasterDataset = rWorkspace.OpenRasterDataset(Filename)
Dim geoDs As IGeoDataset = DirectCast(rDataset, IGeoDataset)
'Assign extents to variables
coordXMax = geoDs.Extent.XMax
coordYMax = geoDs.Extent.YMax
coordXMin = geoDs.Extent.XMin
coordYMin = geoDs.Extent.YMin
'Test
MsgBox(coordXMax)
End Function
So, I didn't have the .NET SDK installed. Whoops. Once I got the ESRI.ArcGIS.Version.dll file referenced in, everything worked juuuust fine. I still need to add some more stuff in, but this is what I was getting stuck on.
Thanks everyone for your help!