First off, it doesn't feel strange to me. I would feel comfortable using this (English) sentence, even though the bus stop is actually located five houses away.
As for "at" versus "near", I'm going to assume that you're giving directions here. So, that person is going to have to get off the bus "at" the stop. Even if it's only an imaginary stop while trying to visualize where you live.
Points made, but if giving directions, I would simply say "get off at the eighth stop" not that I live there. And even still, "I live near the eighth stop" implies that one would have to get off at that same stop.
It's probably just a regional difference or the like (arguably nigh all of these little debates are), but for me, personally, "at the stop" would be a lot more ambiguous and/or unclear in comparison to "near" or "next to" or "in the vicinity" etc.
Or busoa haltejo. But it might be metrohaltejo or fervojoa haltejo, even troloa haltejo, I guess, or funikulo haltejo or possibly even pramŝiphaltejo. Even aeroplanes and zeppelins could possibly have designated locations where people could get on or off.
The reason that the speaker doesn't specify the type of stop is that, in these instructions, the sentence before this one told you to take some rimedo de transportado. Since you already know what means of transport you'll be on, there's no reason to mention that again.