More connection to Bitcoin you say, what can be more connected to Bitcoin if it isn't currency/payment gateways. For a business Idea I can only think about selling branded fashion wears with Bitcoin logo printed on them or popular occasion in the history of Bitcoin or phrases like "I'm hodling". Basically I think the best thing to do is to do any business that can succeed in your geographic location and accept Bitcoin as a payment option. This is the best  Idea I can come up with because I don't know what sells in where you are from so I shouldn't be giving you a business with idea that might work only in my region and not yours.

Running a business at losses shouldn't be an option just because you want to promote Bitcoin, you should be making profit and be promoting Bitcoin at the same time and you won't get tired of running your business because you're doing what you love to do and making money from it. If you really what to get into business connected with Bitcoin then start up a business that helps spread the awareness and adoption of Bitcoin.