On discovering that Marianne is recovering he clearly states that;

"Had I known as much half an hour ago -- But since I am here"

So even half an hour ago would have been enough for him to turn the other way to Combe Magna (?) where he had business.

His visit was prompted only by the news of the impending death of Marianne.

I have divided his visit into stages depending on his responses.

Stage 1
He came to beg forgiveness at Mariannes deathbed. A true 'sensibility' style/melodramatic scene. It would do his pride good to see her forgiving him and her love for him shining in her eyes.
It was the same on an earlier occasion when he went to Barton Cottage to tell them he was going to London.

"Why did you call, Mr. Willoughby?" said Elinor, reproachfully; "a note would have answered every purpose. Why was it necessary to call?"

"It was necessary to my own pride. I could not bear to leave the country in a manner that might lead you, or the rest of the neighbourhood, to suspect any part of what had really passed between Mrs. Smith and myself,

Stage 2
oops!! She's recovering. Had he but known about half an hour ago - he would have changed directions? Now what? Lets turn on my charm, it always works.

"For once, Miss Dashwood -- it will be the last time, perhaps -- let us be cheerful together. -- I am in a fine mood for gaiety. -- Tell me honestly" -- a deeper glow overspreading his cheeks -- "do you think me most a knave or a fool?"

I'm astonished (along with Elinor) at this kind of talk.
It doesn't seem like he wants to talk of forgiveness.
That's not working he thinks.

Stage 3
Elinor gives him the lead since he doesn't really know what to say.

"Is this the real reason of your coming?"

How can he say what he wanted to say to a dying Marianne, vulnerable, and carried away by passion?
He tries his charm again, mingled with a demand for sympathy, and a *lie*!
Lets pretends to be drunk to cover up the former faux pas.
He thinks his confession of being drunk will sound very charming and naive.
So he replies;

“with an expressive smile, and a voice perfectly calm. "Yes, I am very drunk. -- A pint of porter with my cold beef at Marlborough was enough to overset me."

"At Marlborough!" cried Elinor, more and more at a loss to understand what he would be at.

"Yes -- I left London this morning at eight o'clock, and the only ten minutes I have spent out of my chaise since that time, procured me a nuncheon at Marlborough."

Poor fellow. But of course Elinor sees that he’s not drunk.

Stage 4
Elinor persisists in asking the reason for his visit.

What is it, that you mean by it?"

"if I can, to make you hate me one degree less than you do now . I mean to offer some kind of explanation, some kind of apology, for the past -- to open my whole heart to you, and by convincing you, that though I have been always a blockhead, I have not been always a rascal, to obtain something like forgiveness from Ma -- from your sister."

So Elinor informs him that Marianne has forgiven him.

He feels forestalled!! Otherwise his job is done and he should go. But no, he wants acceptance and understanding of his behaviour. He has demands for a repenting person doesn’t he?

Stage 5
With a new resolution to approach differently he proceeds with some force.

Now will you listen to me?"

And then we are treated to a very incoherent narration where he ends up baring his soul and character, by sometimes saying things which he thinks he ought to say, and sometimes actually speaking the truth (which turns out to be quite ugly).

His incoherency arises from what Elinor lets drop during his narration. Like;

"You did then," said Elinor, a little softened, "believe yourself at one time attached to her."

Of course I don’t understand Elinor’s question here because he has just confessed that;

I did not know the extent of the injury I meditated, because I did not then know what it was to love. But have I ever known it? -- Well may it be doubted; for, had I really loved, could I have sacrificed my feelings to vanity, to avarice? -- or, what is more, could I have sacrificed hers? -- But I have done it.

But it is enough to set him off into describing how he suffered.

At the same time his repentant heart can’t stop him from saying;

Honest stupid soul. of Sir John.

Thrice he shows his dislike of Colonel Brandon.

The end says it all. He who pretends to ask forgiveness cannot forgive others, though I see no reason why he needs to forgive Col Brandon. Perhaps he defeated him in the duel!!! :-D

His dislike of Col Brandon (I think it’s him that he means here, I wonder what made him think Marianne would marry Col Brandon)

"But she will be gained by some one else. And if that some one should be the very he whom, of all others, I could least bear -- But I will not stay to rob myself of all your compassionate good-will, by showing that where I have most injured I can least forgive.

How can he feel repentant when he shows such jealousy that he can’t bear to see Marianne married, especially to the man he dislikes.

From which angle does he show any characteristics of a man who wants to apologise and ask forgiveness?

I don't think his long ride justifies believing he had genuine feelings.