No. Not at all.
Baking soda is a leavening agent. Together with baking powder it gives your cake lift and airiness. Bread flour is just flour with a higher protein content. If anything, it will make your cake more dense (though not in such small quantities as you would have for baking soda). If a recipe calls for both baking soda and baking powder, the recipe is balanced to rely on both and omitting one will cause the recipe to fail (to some degree). How it will fail will depend on the recipe, which you haven't included.
If you already have baking powder, and don't have the time to find baking soda, I recommend that you instead find a different cake recipe that uses ingredients you already have at home - specifically one that does not require baking soda at all. Many cake recipes use only baking powder, so this should not be overly difficult.
You may be able to replace the baking soda with baking powder at a powder to soda ratio of something between 2-1 and 4-1 depending on who you ask (e.g. two teaspoons of baking powder for one teaspoon of baking soda). Depending on the type of cake this may create off flavors in your final product. This and other possible substitutions for baking soda in cakes are discussed on this site in the related question: Replacements for baking soda in a cake?
Note, while these options are available to you, I still recommend finding a different recipe, particularly if you're not set on this specific one you're already using.
Also, since you mention bread flour, I hope you're not using bread flour for your cake instead of all purpose flour or cake flour. These three flours are quite different and will cause different outcomes if you use one when the recipe calls for another.