So there is a remedy floating around the internet that states 1 tblspn of baking soda mixed in 8 oz of water results in forced excretion of water soluble drugs. For example methamphetamine. I'm not exactly sure of the specific details on how this recipe for explosive diherrea is able to mask the toxins and their coinciding metabolisms in your urine for a predetermined period of time on a panel UA test. In professional opinion, does this at all sound possible? And if so, what is the beauty behind this freedom saving concoction?
Let us start by saying that it is not recommended to use home-made remedies off of some internet website, as the information may be inaccurate and misleading. You should always consult with a healthcare professional in order to avoid adverse outcomes.
The concept of manipulating urine pH in order to accelerate the excretion of certain drugs is well-known. It is related to acid-base properties of drugs, as most drugs are weak acids or bases (I will not go into detail about this here, as it is a very basic concept in pharmacology, and can be looked up in most textbooks. You can also read a bit about it here).
The mechanism of increasing excretion rate of certain drugs is related to a phenomenon called "ion trapping". Basically it means that since acids will be ionized (become charged) in basic pH and bases will be ionized in acidic pH, and ionized species have difficulties passing through membranes, changing urine pH can eventually cause a certain drug to concentrate in the urine.
(drugs pass from blood to urine according to their ability to pass membranes. In general, if a drug is uncharged it can go back and forth, but if it becomes charged, it would be more difficult for it to move across membranes, so it is essentially "stuck" where it became charged, which is preferably the urine).
In other words, the normal range of urine pH is 4.6-8 (see here), which means that it fluctuates between acidic and basic values (pH value of 7 is neutral). When the urine is acidic, basic molecules that pass from the blood to the urine become ionized (charged), and then cannot go back into the blood (i.e. they are trapped in the urine and are excreted from the body more quickly).
When the urine is basic, acidic molecules that pass from the blood to the urine become ionized and are excreted from the body more quickly.
To address your specific question: The commonly accepted method for making the urine more basic (i.e. alkalinization) is to administer sodium bicarbonate intravenously. I found a study about administering sodium bicarbonate orally, but it is not the common practice. Also note that methamphetamine is a weak base (pKa = 9.87, according to DrugBank), so it will be excreted more quickly by acidification of the urine, and not alkalinization (acidification is usually done with vitamin C).
Finally, I would like to point out that one tablespoon of baking soda in 8 oz of water is not very precise and has a relatively high potential for error, which may lead to too high urine pH. I repeat my warning: stay away from this kind of practice, as unsupervised manipulation of blood/urine pH may have adverse and even fatal reactions.