Darn, another anti-contestshipper -.-
Anyway, I think Drew meant that he wanted ger to go with her heart. You can almost tell that he likes her by the way that he acted, how he always gives her a rose, and that he said that hoped to see her again.
By telling her to go with her heart, I think in fact he meant for her to go with her heart. He doesn't want to be with somebody or keep chasing after them if she's not interested at all, so he probably wanted to know so he could know if he should keep trying or not. There's my two cents ^^;;