What glue can I use to adhere a glass vase and glass bowl together?

GE Silicone II, it's rainproof and adjusts to different temperatures well. It's what I use in my totems and dish flowers.

E-6000 works like a charm

Epoxy with a hardener?

Look for silicone aquarium sealer, it's made to bond glass.

E6000. Two part epoxy may also work.

I use E6000 on almost everything. It will hold many different materials to each other.