To introduce them in a safe way when the cat is feeling up to it; put her in a crate with a towel over most of it so she feels safe and bring the dog around on a leash. KEEP THE LEASH LOOSE!! If you are nervous and so hold the leash tight you will be inadvertently telling the dog that there is something wrong and she needs to be wary. If she shows any type of aggressive behaviour at all - this means woofing or even just staring (difficult I know for a border collie
) give the leash a snap and tell her "leave it" (or whatever command you have that means the same thing) and make her walk away. Only let her approach when she's being quiet and non-threatening. If the cat is calm this works great, if the cat gets nervous and hisses then put the crate in a safe place where the cat can observe the dog without feeling threatened.
To teach a strong leave it command to a dog you should use things that are really something it wants but isn't allowed to have normally, and I like to use a shake can (a tin can with about eight pennies in it and taped back shut). I don't like to use toys because toys are a source of praise and relationship building. I prefer things like food and garbage and other things you never want your dog to touch anyway. One good way is to put some yummy smelling food on the coffee table, point at it while looking directly at the dog and saying in a very commanding tone "leave it" then step away. If the dog goes for it give a good shake on the shake can while simultaneously commanding "NO LEAVE IT". Border collies are sound sensitive so this usually works really fast without any relationship damage. As the "Big Dog" in the house the dog shouldn't even think of touching your stuff anyway and that includes food. Once the dog knows the leave it command you can apply it to your cat. This tells the dog that the cat is yours and therefore off limits.
With a solid leave it command you should be able to leave your dog with almost anything and have it there and intact when you come back. I once had to leave my shepherd mix in the car with a hot pizza for an hour and she never touched it.