well no newborn here and a bullie , but have always had dogs and a couple of newborns .
no contact , sorry dogs eat and lick stuff you do not want near a newborn and a dog will lick a newborn if you are not there to supervise , never leave the dog any dog or cat for that matter alone with a newborn , the dog has no understanding of a newborn the sounds the movements smells ect ect
We always did the blanket thing with all our pets worked well for the animals to get used to the scent of the kids also anytime the dogs were near the kids we always repeated in a level voice not harsh " that's a gentle " I still say that too my Bullies when around cats and new dogs to them and you can see them relax and know that its not to be herded lol .
your dog will be curious that's cool and of course not understand why Mom is all of a sudden very very busy you have to keep them in touch with the new addition to the PACK as dogs are very much a Pack or group of family animal
Bullies are very easy going and gentle but they can be clods and get very excited and there BIG so never leave them unsupervised with a new born or even a toddler Bullies will knock em flying lol
sorry to sound so intense but better safe then sorry in my view , do the blanket thing worked for us very well
AND CONGRATS ON THE BABY so cool !!