Shred cabbage in food processor or using a box grater. Add onion and bell pepper.
Sprinkle sugar, cider vinegar, celery seed, salt, and pepper over cabbage and mix well. You may not end up using the whole teaspoon of celery seed. (I adjust this depending on the size of the head of cabbage, if it is a really big head I use it all.)
Add mayonnaise and mix well. Transfer to smaller bowl as the slaw shrinks once you have added the mayo. Choose a bowl that will allow for a little additional liquid to develop as it chills.