Vinegar is the right reagent to deal with baking soda, but it's not trivial.
The problem is, with it backed up with water, any vinegar you add will be heavily diluted, and won't be able to react with the baking soda. So first, remove as much water as possible. Bail it into a bucket if it's deep. Bailers can often be made from large plastic milk bottles (called "milk jugs" in some places). Soak as much of the rest up as you can with sponges.
If you have any sort of water pump or wet vacuum, use it. A drill-mounted pump can be useful, especially if you adapt the hose down to something small enough to fit into the drain (but of course if it's a mains-powered drill you'll have to be careful with all that water around). You can even syphon from a shower that's raised off the floor.
Then add vinegar as directly into the drain as you can. Again, a thin hose into the drain, connected to a funnel will allow you to get the vinegar right to the plug of baking soda. Add a little, wait a few minutes, mixing if you can, mop/suck up what you can, and add a little more. Take it slowly and gently. Warm (e.g. shower temperature) vinegar will react faster, but that may cause splashing, so mind your eyes.