unless you are beset by gophers, that is correct, no bottom.
I'd rough up (like, roughly dig over with a shovel) the soil underneath so the raised-bed soil can 'merge' with the underlying real soil and make it easier for the plants to sink their roots down deeper into the real soil. Reduces water demand.
I have a question along the same lines if I may ask. Would 16 ft long boards be too long for the length of the bed? I understand to make them wide enough to make them easily manageable, but what about long? Would it be cheaper to buy 16 ft boards or 8 ft boards? We do want a fairly large garden
Some of my beds are 4 x 8 and others a 4 x 12. Sometimes it takes and extra second to walk around the bed. I like to plant in 4 x 4 squares so both of these work well for me.
Ticks, lucky you not having gophers. Maybe you shold come visit me for the weekend and bring your gun.