One practical reason why Jack didn't offer Ennis a ride possibly was that they were indeed heading in opposite directions, even if not for the brief moment Ang Lee showed us.
Assuming Ten Sleep is indeed Signal and Ennis turned towards Riverton, their destinations were opposite from Signal:
So even if Jack had offered Ennis a ride, it would have lasted only a few hundred meters till the next crossing.
But of course there's more to it than that. The opening question has bugged me also for a while, combined with the inevitable "What might have been....."
I think one important reason why Jack acted the way he did is given by Ang Lee himself (paraphrasing): they were
both cowboys. They didn't talk about their feelings; non-verbal communication is important; and they had pride. What's true for the whole movie is also true for this scene.
I think pride was a crucial factor here. Jack already had taken the punch from Ennis earlier, and was apparently and understandably pi**ed about it. Look at his face when they descent with the sheep.
Then, while standing beside his truck, Jack is all cautious and hesitant. And he makes one last attempt when he asks Ennis whether he's going to do this again next summer. And even after Ennis's negatory answer (which wasn't
totally negatory, btw) he half-tries again with "I might be back ... if the army don't get me." He leaves a door open. Ennis at least knows where to find Jack next summer if he wants to.
I think Jack has gone as far as he thought he could without begging. I think to him Ennis seemed to be determined to not keep their relationship in any form. And therefore Jack must have doubted Ennis's feelings, respectively must have assumed it was just a one-shot-thing for Ennis for the summer, as he had said before. Understandable that he didn't ask Ennis anything more, not even offer a ride.
What Jack didn't realise, imo, was that Ennis was almost as reluctant and full of doubt as Jack. He didn't say no to Jack's question of doing this again next summer, he said 'Maybe not.' And he didn't directly go after he had said "Guess I'll see you around." He lingered and waited - for what? Another word from Jack? Another try? Maybe he even hoped for a ride, no matter how short?
Ennis didn't
want to go and leave Jack behind once and for all, he thought he
had to. Big difference.