How sad. I think it is really sweet of you to offer your help. I can't imagine anyone thinking that this is an intrusion. However, I think that most offers to help are never really accepted or taken up on because it is just to vague of an offer. Do you know if he had any insurance? How is she going to cope financially? I would probably give her real help (pay for someone to take care of her yard, gift cards to Walmart, etc.) instead of just an offer of help. Take her meals once a week. Just do it. Don't wait to be asked for something specific. I am sure she will appreciate anything you do to help, but it will probably be hard for her to verbalize exactly what she needs. Also, if your relationship grows at all, contact her periodically to see how she is doing. Be a listening ear. Blessings to you as you minister to her needs.
OH, I just thought of something else. One of my friends lost her husband a couple of years ago. She had two friends come alongside her as she went through the various trials she faced. They were not close at all before the death, but became close quickly after. One thing she told me that was really helpful is that when she had to go to the VA or any other agency to fill out paperwork, etc., one of these ladies told her (didn't ask, but told her) that they were on their way to pick her up to take her. She didn't think she needed anyone to go with her, but she really found that she did. She was sooooo thankful. She said she felt strong at the start of one of her meetings, but then would just break down and weep. Her friends comforted her and also were able to help out with the task that needed to be done. You might be able to accompany her to these things. Or, if you know any of her close friends, perhaps you can share this with them.