You can play with two players, but it's going to take some work
But you will need house rules and it might not work that well
In a video (around 27:45min) on his YouTube-Channel, Adam Koebel himself mentions that
Dungeon World as written does not work for 2 players, like, flatout doesn't. You'd have to change bonds
In the comments on the video he confirms that by "2 players" he refers to 1 GM and 1 Player.
Let's look at why we need to change bonds
This should be easy to answer: Bonds refer to other player characters. Of which there are none. But how would we change bonds, then?
One idea would be to allow bonds with locations - But as stated in the answer to that question, there would be no real way to trigger
Take +1 ongoing to aid or interfere with the target of the bond.
This might be a big problem. My Advise: instead, allow bonds with NPCs that are important in the game.
- At character creation, leave the slots for the bonds open
- When the player encounters an NPC he likes, let him write a bond for that NPC.
Please note that this is the way I would do it, after playing with two players only for two or three sessions, ignoring bonds completely. See below for more information on my personal experience
Why do we need bonds?
They are a great way to a) interact with the world around the players and even tell stuff about them (I once ran a con with Boromeo, the Warrior is a great example of that) and b) to gain experience. Both of those work very well with NPCs, too.
The "Provide an Opportunity that fits a characters abilities" problem
The GM-Move I just mentioned in combination with the general problem of having only one PC in your game might be a big problem. The solutions to a problem will not be all that different and thus might either get boring for both the player and the GM, or they might lead to the GM trying to "mix things up" and resulting in the player beeing unable to use his character's abilities to their full extent. As a GM, you have to be aware of that!
If I were to think about it, you could certainly try to a) encourage the player to dabble in the multiclassing-possibilities that DW offers, or even give him one or two additional stat increases and/or moves. I have not done that myself, though, just as a fair warning.
My personal experience with One-on-One DW
I have tried Dungeon World One-on-One for a few sessions, with different characters (but always me as the GM and the same player) - and I was not really happy. First of all, we chose to just ignore bonds, which was a big mistake for the reasons I outlined above. The second problem was that we just would not run into that many interesting situations. Either the player steamrolled through challenges and situations, or he was totally lost with no possibility other than fail. It is really hard to find a middle ground on that (see the "provide an opportunity"-Point I made earlier)
The Internet and a final statement
A quick look around on the internet shows me that you are not the first person to look for help on this topic. And most people seem to say the same: It's not really the perfect game and it will be hard to do this.
You could try, though. Test it out for one or two sessions, think about a way to change the bonds (see my untested suggestions for inspiration) and choose a class that can do more than one thing. I found the ranger to be pretty good at that, if you want to run a wilderness-adventure. The companion is a great thing to have when there is no party. Also, think about Hirelings for the player. You will quickly see if you like it or not. The first one or two sessions should already be a good indication.