Based on your patterns one improvement would be to change to using StartsWith instead of Contains. StartsWith need only iterate through each string until it finds the first mismatch instead of having to restart the search at every character position when it finds one.
Also, based on your patterns, it looks like you may be able to extract the first part of the path for myString, then reverse the comparison -- looking for the starting path of myString in the list of strings rather than the other way around.
string[] pathComponents = myString.Split( Path.DirectorySeparatorChar );
string startPath = pathComponents[0] + Path.DirectorySeparatorChar;
return listOfStrings.Contains( startPath );
EDIT: This would be even faster using the HashSet idea @Marc Gravell mentions since you could change Contains
to ContainsKey
and the lookup would be O(1) instead of O(N). You would have to make sure that the paths match exactly. Note that this is not a general solution as is @Marc Gravell's but is tailored to your examples.
Sorry for the C# example. I haven't had enough coffee to translate to VB.