Transitioning the area is easy. There are a couple charted transition routes. I'm also based in OGD. Although you can go down the east side of the valley and avoid SLC Class B, that area around BTF is a very busy bottleneck of GA traffic. I wouldn't recommend going through there without talking to controllers. You can also fly over the top of the Bravo, but again, I wouldn't recommend it. Remember you've got airline and corporate traffic transitioning the area vertically at 250 knots. Not real smart in my opinion. The backside is an option and is much more scenic, but if your looking for efficiency of time, just fly one of the transitions and be on your way.
So, now more directly to your question, coming from the north, you can either contact Ogden tower or circumnavigate it to the west. If you talk them, request the I-15 transition southbound. OGD will hand you over to Hill tower as you follow I-15 southbound. They will ask you to report 5 miles south, at which time they will cut you loose. They do not usually coordinate a handoff with SLC approach. At this point you are in the area of Lagoon, an amusement park that is also a VFR checkpoint. Heads up here too because in this area the Class B shelves start lowering. At Lagoon get on the east side of I-15 if you've not made contact yet with approach and make sure you are under the shelve. On call up, tell them you want the I-15 transition southbound. They will tell you to fly over I-15 southbound, what altitude, and will either give you a Class B clearance at this time or shortly down the road. As you near the the ridge line that jots out by the capital abeam the tower, Class B goes to the surface. You will normally be given Class B clearance well before this and be switched over to tower if they are busy to transition the portion that reaches the surface. Otherwise approach will keep you all the way.
Once south of the capital, you will be told to stay over I-15 southbound or may be given the instruction to stay over or east of I-15. Depending on your altitude, you may be out of class bravo and depending on the controller's workload, he may tell you to remain clear of class bravo. Not a big deal as you have lots of room vertically and horizontally to fly south and exit the area. Be heads up on Provo's class D south of there.
Unless you're landing at OGD, it may be easier to either circumnavigate OGD and Hill's airspace to the west and make your first call to approach around the Lagoon area as described above. Or, if you are high enough that you'll be in one of the Class B shelves in the OGD area (and thus above both OGD and Hill's class D), just call approach north of OGD and get a class B clearance for the I-15 transition southbound as described.
As was said above, the controllers are good to work with, especially if you come across as knowing what you're doing and are competent. I see a lot of people waste a lot of money and time because Class B intimidates them but this one shouldn't give you any heartburn. Just tell them what you'd like to do and they will help you out.
Feel free to PM me if you have any questions or want me to talk you through it as it gets closer. Happy to help.