I've beaten the first level, and I've had an opportunity to move around the hub area, and I see that there are bonus levels I could walk into if I had the right characters, but it doesn't say I have to have the level packs. Could I just put in Bart and play the Simpsons level, or is there also new bonus level somewhere that requires the homer level pack?
There are three different types of levels.
The main storyline of the game. This is started when a new game is started, and after the first little bit, the heroes make it to the hub area (called Vorton). The storyline is continued by jumping through the portal on the pad in the game. This generally follows WildStyle, Batman and Gandalf's adventures but you can play using any characters that you own.
In the game's hub world, on the floor above the portal pad (accessible from the elevator to the left of the portal pad), there are Adventure Worlds, which are open-world bonus levels for each universe (DC, Simpsons, Portal, Jurassic World...), and those levels require any character from that franchise, be it fun pack, level pack or team pack.
The levels from the Level Packs are accessed by having the character on the pad (in any of the positions), then jumping through the portal. At this point the game gives you the option of continuing the story, or playing the level from the level pack.