Thanks everyone, I used a combination of your responses.
In my app.config file my connection string is defined as follows
<add name="MyConnectionString"
connectionString="Server=.\SQLExpress;AttachDbFilename=|DataDirectory|\MyDatabase.mdf;Database=MyDatabaseForTesting;Trusted_Connection=Yes;" />
In my unit test class I set the DataDirectory property using the following
[TestInitialize]
public void TestInitialize()
{
AppDomain.CurrentDomain.SetData("DataDirectory", System.IO.Path.Combine(AppDomain.CurrentDomain.BaseDirectory, "Databases"));
// rest of initialize implementation ...
}