How should I handle mispronouncing words in a coworker's native language and feeling like I'm embarrassing myself?

I think the best approach would be not to worry about it. At least you're attempting to pronounce them, which is more than most would bother to do. And if you say it wrong, or if you simply don't know how to say it, that's the perfect opportunity to ask him to correct you:

"Hey, am I saying this right?" is a perfectly ok phrase to use.

Technically, I would be fairly concerned about using Swahili in a codebase that will almost certainly be maintained in the future by English speakers, however in general I commend your attitude and behavior here.

One reason, perhaps, that Bob gives up trying to correct your pronunciation is that you're in the middle of, eg, a review not a language tutorial and it's important to make progress on that. Perhaps a separate conversation where you just ask Bob's help on pronunciation and meaning of a word or two?

Also, it's possible that Bob really doesn't have much interest in teaching you basic Swahili, so you might want to try to figure that out. Something like "Hey, Bob, I just sort of realized that I've been asking you quite a few questions about Swahili. I've really enjoyed learning about the language from you, but I just wanted to check that you're actually ok with me doing that?" or something else along those lines.

Remember, too, that the company isn't paying Bob to teach you Swahili and as a remote team member, he may be thinking of that as well. You might check out online resources to learn on your own. There's probably at least a basic pronunciation guide online and maybe some Swahili-English dictionaries. I'm sure Bob would appreciate your willingness to dig in on your own, and you might feel less awkward as well.

Google Translate can speak!

Have your phone handy with Google Translate. You can translate in both directions and listen.

If he doesn't understand your pronunciation even after copying the sound, just tell him the English word.

P.S.

A personal opinion. I don't think jokes about being "too white" are any more appropriate than being "too black". Let's leave race out of business matters altogether. It may (or may not) be acceptable between close friends of different skin colours.

Pronouncing stuff wrongly incorrectly is very very common when learning a foreign language. You are not even trying to learn your co-worker's language, so it is not surprising that you should not get everything right.

You are already going out of your way by trying to learn pronunciation rules, which is nice. You should not feel horrible. Your co-worker probably either likes your wrong pronunciation because it is good for laughs/makes a good topic for small talk/he finds it adorable or whatever, or else he doesn't care. If he would care, he would probably stop using Swahili at some point

The graceful way is just to accept that your pronunciation is going to be wrong 50% of the time or so, and laugh about it. This is normal and by learning some of the simple rules you are probably already avoiding some of the worse mistakes (e.g. mispronouncing the x if your colleague was Chinese)

Was für ein absoluter Unsinn. Wenn er in den USA arbeitet, dann soll er gefälligst die Sprache benutzen, die in den USA verwendet wird. Eines Tages wird dieser Kollege von einem anderen Kollegen ersetzt, der kein Suaheli spricht, und dann stehts Du total auf dem Schlauch. Schlimmer, deine Firma steht auf dem Schlauch. Und dann wirst Du gefragt, warum Du nicht eher was gesagt hast.

And if you didn't understand a bit of this, that's exactly why it's a very, very, very bad idea to let him write code in Swahili.

Your question presents two problems.

1. Your inability so speak Swahili properly. You are already doing your best. Some sounds in some languages are very difficult for people not familiar with those languages.

Example: there are English sounds almost impossible for Russian people (think of word "her"), and there are Russian sounds almost impossible for English people (example: "сын", meaning "son". That middle "ugly" letter in the middle, looking like "bi", represents one sound - for which there is no graphical representation in English). It is neither good, nor bad. It is just the way it is.

2. The official language in your company, and the code writing rules. There should be a clear rule in the company which language(s) should be used in general in official communication, and which languages should be used when writing comments or choosing identifier names in the code. The purpose of those is to help people understand each other. Considering that Swahili is not at all an "international" language, I expect that the company should forbid it, together with everything else which is not according tot he rules. Module names are also included - they help greatly in understanding and navigating the code.

Of course, choosing the name of an application is a different matter - any language can be used, and any word constructed out of thin air.

It is also a different matter if employees choose to learn other languages, including Swahili and Aramaic - that should be perfectly fine too.

Simple, if in doubt, spell the word out instead of attempting to say it.