Which preposition is correct in each of the sentences of dirt road?
- The grass grows on/in the dirt road.
- There is a little bush in/on that dirt road.
Which preposition is correct in each of the sentences of dirt road?
- The grass grows on/in the dirt road.
- There is a little bush in/on that dirt road.
They are somewhat interchangeable, as are many prepositions. In your specific examples I'd go with on:
- The grass grows on the dirt road.
- There is a little bush on that dirt road.
A quick ngrams search reveals that in Modern English, the phrasing on the road is more common than in the road, which is true in AmE, BrE, and English overall
Both usages can be correct. They are not, however, interchangeable. Use "in the road" if you wish to convey that the object is blocking the road, keeping in mind that "in the road" is a shortened version of "in the middle of the road".
In fact, the only time things can be "in the road", is when they are in the middle of the road, figuratively speaking. Things can never be "in the side of the road" or "in the edge of the road". Although they can be "on the side of the road" and "on the edge of the road".
Use "on the road" if the object is expected to be on the road.
One drives around that which is in the road. One drives over/past that which is on the road.