I lived on Blvd. de Port Royal for two years, so I am familiar with the area. The RER B is the most crowded of all the RER lines. I would avoid it with luggage at rush hour. On the other hand, the 38 bus route begins at the Gare du Nord and will drop you right where the Port Royal RER station is. This route runs parallel to the RER B from Gare du Nord as far south as Denfort-Rochereau, so you may end up using it a lot during your visit to Paris. At "Observatoire-Port Royal", which the stop is called on the bus, you only have to head east across the street and go two very short blocks to your hotel. The bus is better because it has an area in the middle for large items. This is where you would stand with your luggage, or perhaps sit on the pull-down seat if it's not too crowded. This area is for wheelchairs, strollers, shopping carts, luggage.
Finding a bus stop in a new city can be a bit trickier, but from what I could see on line, the bus starts off from the street to the east of the station and turns onto the same street running in front of the station. Coming out the main entrance, you'll be walking south, so you'll turn to your left to find the stop. It could be one or two blocks. (The 38 used to end at the Gare de l'Est, not Nord, so I've haven't caught it there.) On the front of the bus you want the one that says "Porte d'Orleans." From time to time the buses may say "Luxembourg" or "Chatelet". Those 38 buses will stop before getting to Port Royal, and you'd have to change to the next bus, a bit of a pain in the neck. In this case, just wait at Gare du Nord for the next 38 bus because chances are it will probably say "Porte d'Orleans" and be running the whole route.
If you google 38 bus paris, you'll get more info. Here's some trivia: the route the bus takes is the main road the Romans created to bisect the town.