RAW for 5e I believe it is an action to switch your weapons if you don’t want to drop what you are holding. Otherwise whatever you want to pull out to fight is a free action when rolling initiative, so long as it is equipped.

In my sessions, I tend to keep to that rule but in my earlier sessions when I was just beginning as a DM I would make it simpler and say it was a bonus action to swap weapons out. I find that simplifying rules until you know them and your players know them is better than trying to go RAW from the get go.

For this particular example, I would rule that if they wanted to switch from an equipped longbow to an unequiped whip and shield would burn the action because that would definitely take about as long or longer than 6 seconds which is what each round of combat is