I have 2 sbt's and a cat :)
The cat was here first and dont our dogs know it

He loves nothing better than to sit on the worktop in the kitchen deliberately winding them both up :)
They are both very good with him but when he is down on the floor, Stink (5 months old) can be a bit overbearing for him so we have a safety gate on the stairs so Kitty (aka sh**tty,as other half likes to call him) can have the full run of upstairs without them bothering him.
He still likes to spend time downstairs with us and the girls only bother him for about 10 mins and if he doesn't run off they get bored.:)
So as the others suggested a safety gate is a good idea for when they are alone.
Also while you are there I would just let your dog sniff your cat out for him/herself as cats are quick and if he/she doesn't like your dog or they are to overbearing for it ,it will just make a sharp exit.
Goodluck. :)