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.