How long until a pokemon respawns in the same spot?

It seems that pokemon tend to spawn in the exact same spot. From both my house and my workplace different pokemon keep appearing, but they always pop up in the exact same locations over and over again.

How long after I have captured a pokemon in a certain location will it be until another pokemon shows up?

There is no way to know.

Pokemon spawning is somewhat random. Even at the animated grass icons, which represent better chances of finding a Pokemon, there is still no guarantee you will run into one.

You can check "Nearby Pokemon" through the tab to the bottom right, to at least get an idea of the current Pokemon congestion. If 10 Pokemon show as "nearby", you have a better chance of running into more Pokemon than if it only shows 1. It is still no guarantee.

That said, if you go to an area with higher traffic¹, you have better chance of running into Pokemon more frequently. In fact, when I go to the nearest train station, I almost always run into Pokemon in groups.

You can also increase your chances with the use of incense, or by using a Lure Module at a PokeStop.

_{¹ "Traffic" referring to the means in which Niantic determine Pokemon spawn rates. Areas with higher traffic have higher spawn rates.}