You can do something like:
searchstrings.Find(Function(f) s1.Contains(f))
The following is a complete sample.
Dim s1 As String = "RedGreenBlue"
Dim s2 As String = "BlackWhite"
Dim searchstrings As New List(Of String) From {"Blue", "Orange"}
Dim v As String
v = searchstrings.Find(Function(f) s1.Contains(f))
Console.WriteLine("Found {0}",If(v Is Nothing, "nothing", v))
v = searchstrings.Find(Function(f) s2.Contains(f))
Console.WriteLine("Found {0}",If(v Is Nothing, "nothing", v))
See FindStringInArrayInStringVB for a fiddle you can use to try it.