Bishops hate working alone and love working in pairs. Put them next to each other and they build a fence across the whole board that no king can cross.
g That is the whole idea. The bishops make a wall, your king pushes from behind it, the wall advances square by square, and the lone king runs out of room in a corner. Nineteen moves at most from the worst possible start, and any of the four corners will do, which is what makes this ending far friendlier than bishop and knight.
Driving him to the edge
Keep the bishops side by side, on adjacent squares of a rank or a file, so that their diagonals cross and there is no gap to slip through. Then move your own king towards the lone king rather than towards the corner. His king can only retreat along the wall, and every time your king gains a square you slide the wall forward with it.
Do not chase him with checks. Checks are how you spend twenty moves getting nowhere with any of the basic mates. The bishops are fences here, not weapons, until the very end.
The final picture
The mate itself is worth memorising as a shape, because you can then aim for it from a long way out. The lone king sits in the corner, one bishop checks along the long diagonal into that corner, the other bishop covers the square next door, and your king guards the two remaining flights.
Look at how little work the bishops are doing at the end. The white king on g6 covers f7, g7 and h7 all by itself. The light bishop on d5 covers g8. The dark bishop on e5 gives the check. Three pieces, three jobs, no overlap.
I will be honest about the difficulty. The first time you try this against a defender who runs sideways rather than into the corner you will wander, and that is normal. Set it up with the bishops on c1 and f1, your king on e1 and the black king on e5, and mate it three or four times. After the third attempt the wall stops being an idea and starts being something your hand does. And if you are choosing which minor pieces to keep in a real game, the reason strong players fight for the bishop pair is exactly the coordination you have just practised.