This part of API is not well documented. But here is the code sample, how to access this value. Perhaps it can be simplified or improved
Dim part As PartDocument = ThisDoc.Document
Dim activeAppearance As Asset = part.ActiveAppearance
For Each assetValueInActiveAppearance As AssetValue In activeAppearance
Dim colorAssetValue As ColorAssetValue = TryCast(assetValueInActiveAppearance, ColorAssetValue)
If colorAssetValue Is Nothing Then Continue For
If colorAssetValue.Name <> "generic_diffuse" Then Continue For
Dim connectedTexture As AssetTexture = colorAssetValue.ConnectedTexture
For Each assetValueInConnectedTexture As AssetValue In connectedTexture
Dim filenameAssetValue As FilenameAssetValue = TryCast(assetValueInConnectedTexture, FilenameAssetValue)
If filenameAssetValue Is Nothing Then Continue For
If filenameAssetValue.Name <> "unifiedbitmap_Bitmap" Then Continue For
Logger.Debug(filenameAssetValue.Value)
'Value is read/write
'filenameAssetValue.Value = "C:\path\to\your\texture.jpg"
Exit Sub
Next
Next