I hate asking for help. This is partly from my own desire to appear strong and capable and partly from social anxiety and partly from something else that I haven't quite figured out yet, fear of being a bother to anyone, thank you, Jewish guilt?
It's so much easier for me when people offer, and I can choose to accept or decline their help. But offering is fraught with its own hazards. How can you know that someone needs help, wants help, will accept help? Without being able to experience the situation the way they do, you can't know how they will experience your offer. Imagine someone who is blind or has low vision. It might be tempting to reach out and guide this person across a street or to a seat on a bus. But how frightening it must be to have someone touch you when you literally don't see it coming.
Mr. Rogers told us that we ask people if they want help before just straight out giving help. Unless they're in imminent danger, most people want to show that they are independent, strong, capable. Let them be all those things, but offer help if you wish to.
Some people get incredibly, inexplicably offended when we refuse their help. They feel, I am offering, I am leaving my own little bubble of isolation to connect with another human being. How dare that person refuse my connection? Stated that way, it becomes obvious that they are helping, not out of a selflessness and love for others, but to satisfy their own need to be needed.
There is nothing wrong with wanting to feel needed and valuable. One of the greatest helps I have ever been given was for a friend to ask me for help during a time when I was unemployed, depressed, and feeling useless. The opportunity to be of use to someone probably benefited me more than any help I was able to give her.
Ultimately you have offered; you have made an effort toward good. That effort exists, whether the other person accepts your help or declines it. And that effort is enough.