Most of the problem is anxiety. As with anything new, you'll get over it as it becomes familiar. Be patient with yourself.
The bus is late, again, say 'Not again! Are the other buses always late?'
Their fingernail polish catches your eye, say, 'hey - that's great. I love the color/design/etc.'
People don't always respond, some might even look at you strangely - oh well!
Why do you assume you're someone worth having a random conversation with at all? This is a sincere question.
In my experience of people trying to engage me in conversation, none of them are worth the time. At best I've had a social interaction that basically amounted to being on hold on the phone for five minutes while I struggle to work out what these people want and I'm usually left none the wiser; at worst I've had to listen to idiots segue from discussing the weather to holding forth on a variety of lunatic-fringe causes. Time wasted.
On the rare times I've tried to engage people in conversation they react like I would: impatience that I'm wasting their time, and/or blank looks.
I'd really discourage anyone trying to randomly engage people in conversation unless you're sure you really have some kind of shared interest. IE, you're at a gig, you might imagine then that you could have a meaningful conversation with someone there about the band you are both there to listen to.
I find it relatively easy now to find points of commonality with most people I talk to. Some of this could be explained by the value I place on the intangible feeling of understanding and being understood might be an outlier too.
You're absolutely right too in that if you're repeatedly not clicking with someone it probably isn't worth it to keep the conversation going, but even then there are exceptions. I've seen it take several attempts before a conversation takes flight and sometimes even then it dips back into the mundane only to pick back up again a minute or two later. However, people are much less likely to try to find common points of interest if the person they speak to assumes they're an idiot.
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> On the rare times I've tried to engage people in conversation they react like I would: impatience that I'm wasting their time, and/or blank looks.
> I'd really discourage anyone trying to randomly engage people in conversation unless you're sure you really have some kind of shared interest.
In my experience, the conversations are almost always very positive. Others report positive experiences and find it worthwhile. That suggests you are sadly missing something. The odd thing is, you seem to want to stop others from having these positive experiences.
I reject any question about my worth or anyone's 'worth'. Perhaps part of the problem is that you are thinking about 'worth', and so judgmentally and dubiously, that people don't respond well. People pick up on those signals; they respond poorly to being judged. Or perhaps you are judging your own worth, which would be sad.
I find that my attitude and emotion greatly influences how the conversations go. Especially, give people space to flourish, be curious about them, and you will be amazed at what is inside - worlds of knowledge, insight and creativity that you never imagined. They are in you too, I'm sure.
Random people coming up to me, usually stating something perfectly obvious that doesn't need stating ("Cool Hat!/Hey it's Hot Today/How about the footy eh?"), and then trying to converse on a variety of boring subjects (the weather/politics/footy/where I bought my hat/vaccines are evil/Jesus Christ is Our Savior) is a colossal waste of my CPU time.
Don't be that annoying person. Live and let live.