Nevermind, I found the solution:
Dim epiSession As Ice.Core.Session = New Ice.Core.Session(userName, password, "", Ice.Core.Session.LicenseType.Default, exePath, False, "AGM", "MfgSys")
Dim epiLaunch As Ice.Lib.Framework.ILauncher = epiLaunch = New Ice.Lib.Framework.ILauncher(epiSession)
Dim myUD09 As Ice.Adapters.UD09Adapter = New Ice.Adapters.UD09Adapter(epiLaunch)
myUD09.BOConnect()
Dim args() As String = {"Test1", "", "", "", ""}
myUD09.DeleteByID(args)
myUD09.Update()
I was having trouble getting DeleteByID working, which is why I posted the question. It turns out that I need to pass in all five Keys as an array to get it to work (even if four of the keys are blank).