BHTV on Roku? (or any OTT platform for that matter?) Likely not April 12th, and now with the Charter purchase announcement coming to light, probably not anytime soon. Additionally, one probably can't watch many of their desired networks via the app or the website when away from the home, because the out-of-home viewing options on BHTV are still somewhat limited. Still, it's good to have at least something related to paid TV cable service to watch on the go I suppose.
In your situation, I'd get a Slingbox Pro HD (older gen, retails about $69+/- lately) from Tiger Direct and hook it up at your regular residence. Then, (unfortunately), plop down the $15 or whatever it costs to purchase the SlingPlayer app for your smartphone device of choice, because you'll need it for what comes next. Hook the Slingbox up in tandem with your cable box at home, in the middle between your c-box and TV using either composite or component (component recommended for HD) and test it before it you leave on your smartphone.
OK..Still with me?
Once you get that working to your satisfaction (with the included IR blaster which lets you remotely access your box's on screen guide, change channels, hit Start Over, access DVR, etc. etc.) ... THEN.... (Still with me?) Next, you can load the Slingplayer Roku Channel onto your Roku. Open the Slingplayer mobile app and join the same Wifi network your Roku is connected to, and press the button on your smartphone to "cast" your Slingplayer stream to the Roku.
1) It's a pain in the ass. Especially the first time around, before you get accustomed to the setup.
2) It's not perfect, and eats battery on phone if not charging, requires Wifi at your rental, not to mention bandwidth on said Wifi to be readily available for consumption.
3) However - if done right and that guy Murphy's law is on your side - you're watching live TV on your Roku, or live DVR even.
You can adjust the quality from your mobile device, and regulate how high quality of a stream you're pulling (read: trying to negotiate from your home's connection) that is being relayed to your Roku. The best part to remember here is, you can watch anything you'd be capable of watching if you were still back home. So a little work and struggle could be worth the trouble, IMHO.
I hope this info helps others, including yourself, who find themselves in such a dilemma.
Byron