Chemical reaction in homemade deodorant
The most likely culprit is something acidic reacting with the baking soda (sodium bicarbonate).

Try mixing separately:


Baking soda and witch hazel
Baking soda and aloe vera gel


My guess is that one of these two has an acidic buffer in it that's causing the baking soda to turn into a science fair volcano on you. 

You could try adding some calcium carbonate to the mix (crush up an antacid tablet, or buy powder from somewhere). $\ce{CaCO3}$ is more basic than $\ce{NaHCO3}$, so it might neutralize enough of the acid that it avoids the foaming.

Sodium carbonate, often sold as "washing soda", is essentially a more-basic version of baking soda and might also work.  You have to be careful not to add too much $\ce{Na2CO3}$, though, because it could make the product too alkaline and thus irritating to the skin. In particular, do not substitute washing soda for all of the baking soda—only add the amount of washing soda needed to prevent the frothing.

There are harsher chemicals that you could use to neutralize the acidity, but I wouldn't recommend trying them in a household project like this.