Just to add, true espresso in the manner of how it was developed in Italy, is foremost a science, with the taste-smell senses also adding their 02 cents.
It's a precise mixing of water pressure in bars of pressure, at a tight tolerance of water temperature, tamp pressure, the size and consistency of the coffee grounds, and a precise amount of time and quantity of water flow. As well of course the whole entire process of the coffee beans themselves before they even reach a caffè (soil, sun-shade, arabica/robusta, roasting). There is an official organization in Italy that regulates these standards from points within the caffès and the more popular "bars" go by these standards.
I have spent some time on coffee farms as well in caffès in Italy and partake in this craft somewhat.
Just wanted to add this side of things in case people have been able to experience the bliss of a quality espresso (& cappuccino) from an Italian bar (or of course other locations) and wonder why it can be quite difficult to replicate, from the first sprout of the coffee plant to the crema on your tongue, it's a very long and very complex process, where there are potentials at any step for wavering too much.
PhilipDT's post above mentioning the errors definitely will yield something very different from espresso. Espresso is certainly not just a small amount of coffee.
There are many nice looking cafes around in BA, nice atmospheres, but I certainly do not expect too much. Obviously, there are some to be found serving up a good shot. In the time being, basic coffee will work for me. I have a really nice machine and grinder in my house elsewhere and I'll just appreciate that much more when I return to them.
To reference to main subject of this thread: "stovetop espresso", not to be a stickler, but technically it's an oxymoron. Here's why. As mentioned at the beginning of this post, about true espresso. I'm being technical here, but espresso is one thing, a small amount of coffee is another. For example, many Italians in Italy use "moka" pots for the stovetop as not everyone can afford a nice machine, and they all know this is not espresso, but makes up a decent shot of concentrated coffee.
One many reason you'll never get true espresso from a stovetop is that mostly all of them, if not all, operate on steam generated from the stovetop heat and this will never build enough bar pressure to extract the essential oils from the coffee, yielding a proper crema and a proper espresso. As well, they can not regulate properly the water temperature, so either the coffee grounds get scolded, or too cool.
Typical with unregulated pressures, the coffee is either over or under-extracted. Weak, or bitter.
Like I said, it's all quite complex.
Most people couldn't be bothered with all of this, but only wanted to put it here for reference in case anyone was interested.
Obviously too an internet search will yield tons of info.