When you talk about beta testing, I don't know if you mean closed beta. If that is the case, you can focus testing on particular parts of the game, which also means you may ask the testers to do certain things (such as use the bus). In this enviroment it would be ok to give them the money for the bus.
Otherwise, we are talking about open beta, and people will do whatever. Including going to the empty land even when they have money for the bus.
If you are considering making the bus free to give a better experience to beta testers, you should also consider make the bus free in the final game. After all, the purpose of the test is to find ways to improve the final game. An improvement for the test should be an improvement for the final game.
Evidently, the game is subject to change. Consider if that if you are planning to make temporary changes to ease beta testers, perhaps the game is not ready for beta.
On the other hand, testing is useful at every stage of the game, you should not be ashamed※ of an incomplete game when evidently that is what beta tester have signed for.
※: It is impossible to fix everything; every video game company has released games with bugs. And testing can be ridiculous, even tedious... but without it, things would be worst.
You know that this empty land is a problem. It is a known issue. You will be fixing it before or after testing. Do not hide it. Think that even if you make the bus free, a good tester will try every option, and thus will wander into the empty land.
Aside: I am guessing you have grand plans for the empty land. That sounds too ambitious! You could have created the game without the empty land, being the bus the only option... and then, when you have created whatever plans you have for the empty land (which would no longer be empty), you can introduce it to the game. Regardless, you have the empty land there. Let the feedback come.
So, I suggest to not introducing temporary changes. That includes making the bus free or giving free money. Instead, be clear with the beta testers about what they are going into. That may include telling them what the route is in the long walk. In fact, it is a good idea to provide manuals for an open beta, where you explain the game.
As an alternative to beta testing, you can do blind alpha tests. In that case, you have people in a controlled environment where you can supervise them. The idea is to see how the player reacts to the situation first hand (that is much more reliable than their account of what happened). This kind of testing is great for discoverability. Consider that perhaps players will not know that they have to take the bus, or that the empty land only takes them to the same place the bus does.
As per beta testing. People will probably provide feedback about the empty land. Be ready to receive that feedback. The mitigation is including it in manuals as mentioned above.