You can absolutely camp in a pop-up on the way to Alaska and IN Alaska. No worries about bears if you keep a clean camp.
There are very few campgrounds in Alaska that prohibit tents or soft-sided campers. I never found one when we lived there, and we camped all over the state.
The bears in Alaska generally have enough to eat in nature and do not bother campers. There are many, many people who LIVE in Alaska and camp in tents and soft-sided campers without a problem. I know multiple families that LIVE in a tent ALL SUMMER LONG until the campground closes, in salmon territory. Never an issue.
While I am sure, over the years and thousand upon thousands of campers, someone's camper or tent has been invaded by bears in Alaska, it certainly has not ever resulted in death or injury, at least not that has been reported by the media. Now, if you surprise a momma bear while you are jogging, hiking or biking, things may not turn out so well. Or if you crowd a bear to get a photo...
2012 Dutchmen Voltage Epic 3795
2010 Dodge 3500 DRW MC
2009 GMC 2500 DA CC
2012 Smart-for-two (sometimes hitches a ride in the Voltage!)
2005 Sundowner Sunlite 777