While he is desperate to be close to her, if he gets too close there is the risk that he will lose control and bite her - turning her into a vampire too or, worse, killing her.
He wants her to remain human, but she wants to be a vampire like him because otherwise she will grow old while he remains 17 for ever.
When they first kiss, the chemistry between them is so electric that Bella nearly passes out and Edward has to throw himself away from her so he doesn't ravage her.
His longing walks a fine line between sexual thirst and, well, literal thirst for her blood.
It encourages them to make time for romance, not just sex.