What I do is I freeze bottles nightly, and I put them in the same location in the shade every day

Initially I put a sign that says "water" but it only had to stay up for a week.

Word spreads on the street fast. Once a couple people know, everybody will know. Either by being watched, or due to the nature of vulnerable people to willingly share with others.

If I load up my little buggy with an ice chest and water bottles, what would be the best way to get people water?

just go right up to them and ask them if they have had enough water today? Wear what you normally would wear.

don't ask them a normal question that gives them an easy yes or no, they are going to be paranoid of you most of the time (no matter what!). If you want to build trust, don't mention anything religious. so don't wear a church thing, unless you want to represent all the bad religion someone might have experienced.

so just approach them with all honesty and tell them you want to make sure they have some water and that you hope you can do just a little something to make their day easier

I live in a town with lots of homeless. I also lived in downtown Seattle right near lots of homeless. I always have a rule that if I see someone that needs the basic life requirements, I will ask them and provide what they need. But I will never give them money. I have purchased shoes, coats, and lots of meals.

One day I was speaking with a guy and another one guy that I have helped in the past came and told this guy, maybe his friend?, "don't mess with him, he feeds people"

and it was something I will never forget

other regulars don't ask you for change when you get that kind of reputation

You can get in contact with food not bombs.

They are spread worldwide, and are the experts on the topic.

Also it is great that you are doing this, faith in humanity restored!

I’ve thought it might be good to wear some kind of church’s shirt or something - I know that police tend to fuck with people who help the homeless, especially in my area.

As someone else mentioned, this might actually work against you.

With regards to police interference, if you feel you are able, it's worth pushing back against it. If it's not against the law where you live, record any interaction with police on your phone, and know your rights regarding stop and search, detainment, etc. Legally resisting this kind of police overreach has a big impact on increasing the safety for other outreach groups and can embolden others to make positive change if they're more confident they're not going to be harassed by police for doing so.

We have a program called the resource center that provides additional needs for homeless such as sanitary pads toothbrushes toothpaste hair care products soap and sunscreen. Maybe you can partner with a local program like ours and deliver those packages along with water.

Check with your local family friendly establishments like zoos or museums (or even hotels) if they have any old lost and found items they'd be willing to donate. That can be a good way to get reusable water bottles, hats, and umbrellas. Just keep in mind that many of them may have existing partnerships for this so if they refuse you can try to see if/who they work with and join forces with them.