Hear me out. Its not just social awkwardness. You're experiencing class boundaries and do not seem to have the right mentality to bridge the gap.
First, you call homeless people bums, which sets the stage for how you see and treat them.
I'm an excellent engineer, but I was abused and impoverished as a child, homeless as a teenager. During my 20s, I started a few companies but my savings have been continually depleted taking care of family members. I don't have a sports car or a big bank account, or nice cameras. When I see a stranger or homeless person, I smile and wave. I keep cash on me so that I always have some to give out. I buy people lunch and sit on the curb eating with them and attempting to understand them. I learn the names of my local homeless folk and ingratiate myself in the community. I've moved to a few cities so I've had the opportunity to do this a few times.
I don't do this because I lack social anxiety; I sometimes have extreme agoraphobia, to the point that I have to hype myself up for hours just to go to the grocery store, and I have to wear noise-cancelling headphones to reduce the amount of stimulation. I have PTSD. I'm an extreme introvert. A hermit at times.
But what saves me is the philosophical understanding that I have a duty to the social contract. That empathy and direct aid are nonnegotiable parts of being human. I've been homeless and I know what it's like to be truly hopeless and live a life of uncertainty, fear and hunger.
You need to bridge that gap. Class-induced anxiety is real and I acknowledge that it's probably difficult, but it's not an excuse. You sound like you're in a position to change someone's life. Taking those steps might change your own life.
I get it, but $5 to change someone's life?
It's funny there was a moment I was at a bus station, somebody asked me for money and I dumped all the coins I had in my wallet in their hand for future bus rides. And some lady comes up to me jokingly like "you handing money out? what about me".
But yeah I think I should just give the money out, I think aside from the guy at the red light that's there almost everyday when it's warm, it's rare I encounter somebody personally. Until I go into the city.
> I buy people lunch and sit on the curb eating with them and attempting to understand them.
I clearly don't have the same people on the street as you do. You should not be just sitting down and having lunch with people who are having daily psychotic breaks or are otherwise aggressive. You can't have a conversation with someone who is constantly riding the line of ODing. I have a regular I see who runs around in the road screaming at cars and people.
The very incomplete "down on their luck" view of homelessness is killing progress in my city.