He doesn't consider several other seemingly viable options for achieving his goal, such as contacting someone else with the power to intervene, stealing/destroying Harry's school stuff (his wand!), making Harry too sick to attend, or getting Harry in serious trouble with the ministry/school (e.g. put magical contraband in his house, then contact the authorities).
I'm not sure stealing Harry's school things would have been any more effective than stealing the letters - Harry could buy them again with little hassle, and it would be a lot more obvious that something was up, rather than Ron and Hermione forgetting about him.
As for stealing his wand, I think this would have extremely serious consequences for an elf, and is not something that would be taken lightly. When Winky apparently steals Harry's wand, there is outrage from the ministry, and she is dismissed. Dobby was still employed/enslaved at this stage, and had much more to lose.
Despite having observed Harry, he thinks that making him think that he doesn't have friends will make him not go to school, something that he's presumably got no choice in and is unlikely to pick over staying with people that he obviously hates.
Dobby's premise is that Harry goes to school for his friends, when he really goes for a surrogate home. Dobby is from a Slytherin household, where maybe having support from cronies is a lot more significant. It's not necessarily apparent that Harry hates the Dursley's - in fact Dobby as a house elf may consider his treatment quite civil compared to his own! Muggles are strange creatures, and both Harry and Dobby are victims of abuse which may alter their perspectives.
He thinks that Harry will believe that his friends are capable of forgetting one of the most famous characters in the setting, Harry Potter.
Harry still doesn't have a full impression of how much he is idolised among the wizards, and indeed Harry did consider that Ron and Hermione had forgotten him. So this part of the plan actually worked:
"But the long silence from Ron and Hermione had made Harry feel so cut off from the magical world, that even taunting Dudley had lost its appeal. And now Ron and Hermione had forgotten his birthday. What wouldn't he give now for a message from Hogwarts."
– Harry Potter and the Chamber of Secrets, Chapter 1 (The Worst Birthday)
"See what it's like here?" he said. "See why I've got to go back to Hogwarts? It's the only place I've got – well, I think I've got friends."
– Harry Potter and the Chamber of Secrets, Chapter 2 (Dobby's Warning)
What didn't work was that Harry would refuse to go to Hogwarts as a result.
He somehow thinks that getting Harry in trouble with muggles will make him not want to attend a magic school that's far away from them.
Dobby's original plan was to dissuade Harry - when this didn't work, he tried to get the muggles to ground him and therefore prevent Harry from getting on the Hogwarts train. By causing magical trouble, he hoped the muggles would stop Harry going back to Hogwarts - this also worked:
"You didn't tell us you weren’t allowed to use magic outside school" said Uncle Vernon, a mad gleam dancing in his eyes. "Forgot to mention it... slipped your mind, I daresay."
He was bearing down on Harry like a great bulldog, all his teeth bared.
"Well, I've got news for you boy. I'm locking you up. You're never going back to that school, never. And if you try and magic yourself out, they'll expell you!"
– Harry Potter and the Chamber of Secrets, Chapter 2 (Dobby's Warning)
Judging by how long he has been stealing the letters for, he has been preparing to talk to Harry for weeks, but somehow didn't even know where to start when they began talking.
Dobby hero-worships Harry, and so it is perfectly reasonable for him to be speechless! If you meet your favourite celebrity even after longing for such a chance, you would probably be a bit lost.
You have to remember also that he is bound not to disobey his master's wishes, and he's already flexing the rules considerably in turning up at his house. Some things he couldn't say outright, so he reverted to cryptic clues instead:
"Not — not He-Who-Must-Not-Be-Named, sir —"
But Dobby's eyes were wide and he seemed to be trying to give Harry a hint.
Harry, however, was completely at sea.
– Harry Potter and the Chamber of Secrets, Chapter 2 (Dobby's Warning)