Can I put the bed outside?

Yes BUT only if it is fully protected from the weather, especially rain.
The pet bed fabric isn’t waterproof so if the beans become soaked they are fairly hard to dry out.

The Inner Mattress can be hung in the sun by the tabs, preferably with a bit of a breeze, and the beans will eventually dry out but it is something to be avoided.

The Poly/cotton fabric is primarily designed for interior use and clothing. It will tolerate the outside elements but it’s life span will be shortened and the fabric will fade.