There are a couple steps to climb to aboard a bus. So, it's a matter of lifting up the cart and making sure the cart and the jumbled assortment of bags will fit through the narrow bus aisle to get to a seat.

There have been times I had to put stuff into the bus in segments, a couple of bags dumped onto my seat at a time, go back to the curb for the rest I placed right in front of the bus door. I tell the bus driver I'm going back for those bags. I make sure I'm the last one on the bus so no one is waiting behind me. Unloading is the same way, telling the driver I still have a couple bags on the bus. Dumping my bags right onto the curb by the bus door and running back in for the rest. Then, once the bus is gone, slowly loading the cart up Tetris style and bungeeing it.
OR, I'll try to stow the cart in the cargo hold - that's IF it's the kind of bus that has one. I usually don't have the strength to lift the cart up and in by myself. And I don't want to rely on a stronger man who can do it, but who may not be there. (And believe it or not, the DRIVER will not load the cargo hold many times.

) Again, I may have to load a couple bags in at a time, and then the empty cart as it goes in sideways, so it doesn't roll around in the hold.
Some buses now have a wheelchair accessible ramp to be able to wheel on a cart. But, it takes up so much time for the ramp to be lowered and raised, that it's a major annoyance to all the other passengers to have to wait through that, when it's not a person in a wheelchair but someone with a bunch of packages. I try not to do that.
As for subways: the subway cars themselves are roomy, with a big door to get in. The newer cars also have areas at the ends for a wheelchair to slide in. That said, it is getting DOWN/UP to/from them underground, is still a problem. Even with all the ADA laws.

LOTS of stairs. The few stations that have an elevator, they never are working when you need it. OR they are working only on one subway platform, in one direction - the one you aren't going in.

There are stairs between the two platforms. Or you have to leave the station by going up stairs to get to the other direction. Usually, you have to walk/wheel to the next stop, or if already on a train, shoot beyond the stop you want to another stop that has an elevator that is working, to take you down to the level of the subway platform going (back in a U-turn) to the stop with the elevator you want.
I've been getting various household items & furniture on a Freecycle-type group for sustainability. It's not as scummy as FB Marketplace. In this group, many college grads need to get rid of the furniture their parents bought for them while here at college, when they graduate and go back home or onto their next journey in life. Usually, the furniture is barely used.

(Everyone shows pictures of their items they are giving away so we know what we are getting when we show up.) I've been fortunate to get some great like new items.
One time, when I was new to the group, I was gifted an Ikea Kallax 2x2 cube storage unit. (Picture below.) But it was in Brooklyn. Empty, the units actually aren't very heavy, especially on my luggage cart. Just big and bulky. I bungeed the Kallax onto my cart, was doing really great wheeling it along the street until I get to the subway station and find the elevator was out of service. AND there was no way to get the Kallax unit through the subway turnstyle to try to hobble it down the stairs. This station was unmanned, so they didn't have a regular entrance door to open and walk through.
The nearest subway station with an elevator was a good 30 blocks away - about a mile and a half away. I usually walk a lot in the city. The Kallax was well bungeed on the cart, so I figure I'll walk it.

What I didn't realize was that part of Brooklyn was all UPHILL!

By the time I get to the station

I was thinking I should have left it on the curb for someone else, and just buy a new one and have it delivered to my home.
Kallax 2x2:
After being in the group a while, I learned that most college students have a Kallax unit they need to get rid of.

It took several months, but I now have acquired FOUR Kallax units stacked as a 4x4 full wall unit, and all the same color. AND people close by me were getting rid of theirs, so I didn't have to subway them again.

(Which I don't think I would have done anyway.) And I have swapped out several pieces of my furniture to incoming college students.

It's kind of a "Circle of Life" sustainability exchange. <cue The Lion King music.

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