You absolutely need an order to give baking soda and water. Your unit manager put their job and license on the line doing so without a doctors order, and I would report it. The only exception would possibly be if the family brought it in and gave it to the resident, but I would definitely chart that this was done so against nurse recommendation.... Nursing 101 - Cover Your Own @$$!
At any rate, does your facility not have standing/pre-printed orders? Most allow the use of tums or maalox as needed per standing order for heartburn/indigestion.
Now say the standing orders haven't been signed or your facility does not have any, then I would offer the resident milk provided they are not allergic and/or on any sort of dietary restrictions prohibiting such. Milk is high in Ca which is the primary ingredient in tums/rolaids. It works wonders for me and I have given it to several pt's with + effect. No need for a doctors order either ;-)