Is it safe to let your new puppy sleep in your bed if he is taking a worm treatment if you are taking chemo?

As far as your personal safety goes, your physician may be the best one to ask about health risks given the chemo and compromised immune system. Humans can contract some of the same intestinal parasites as dogs.
Aside from that, deworming treatments often cause diarrhea. The bed may not be the best place for him.
Follow good hand washing techniques and keep everything clean.
Congratulations on your new pup and best wishes to you.

It's never a good idea to let a puppy sleep in your bed, even if you're both perfectly healthy.

Crate training is the best for both the puppy, and you.

As for your concern, we're dog experts, not doctors. You'll have to talk to your doctor about this.