We don’t want any microbes setting up housekeeping in our sauces, and we want the flavors to remain bright and fresh. Commercial barbecue sauces usually have preservatives so they can keep in the fridge in a bottle with a tight lid for many months, even a year or more. My recipes have no added preservatives.
The good news is that vinegar, salt, sugars, some spices, and other common ingredients have antimicrobial and preservative properties, so they tend to help sauce stay fresh tasting and safe from microbes for months. As long as you keep your sauce refrigerated, you should have little risk of foodborne illness. Just make sure that when you are done making the sauce, you put it in a very clean glass bottle with a tight-fitting lid. I use Ball canning jars and lids and run them through my dishwasher, but jelly jars and bottles from other condiments work fine as long as they are ultra clean and have tight lids. Another good strategy is to pour the sauce into a clean bottle while it is still boiling hot. The heat can help kill any stray microbes from the air.
Oxygen and heat are the natural enemies of freshness, so don’t let bottles of sauce sit out on the dining table for long, and certainly don’t keep them on the shelf next to the grill.
Store-bought herbs and spices are often steam treated or irradiated to kill microbes, but fresh herbs and spices can be contaminated just by airflow or birds or critters, so they pose a small risk. That’s why most of my sauces call for dried herbs and spices.