The Jane LRT would almost surely have to be built underground for most of its length. Given how much that would cost and the lack of intensification on most of Jane at the moment it wouldn't make much sense to prioritize rapid transit there, at least not before resolving the disaster Dufferin already is and will grow even more to be with all the development happening there (the easiest fix there being turn the "Ontario Line" northward from the Ex to run under Dufferin to Eglinton).I believe that connecting HBS (and the future GO station) to Jane station via S. Kingsway would solve a lot of transit problems in the area. Not only for HBS, but also for South Swansea which will add more density in the next couple of years.
At first, I would like to see frequent bus service. However, the best option, I believe, is to build (now forgotten) Jane LRT which would extend to Park Lawn GO station via S. Kingsway. This way there would be more users of the new GO station and HBS would be connected with Bloor West Village, Bloor Subway, Crosstown LRT, and so on.
With the Queensway streetcar, the inevitable shutdown of the remainder of King St. to through traffic and the new GO RER station HBS should be pretty well served by transit in the future. I could see them doing a dedicated BRT route from there up to Kipling Station to link the two growing centres in Etobicoke though.