We’re going through this with my wife, although I’m in full time employment.
There’s a case that’s famous amongst those affected by Theresa May’s horrible spouse visa rules that came in in 2012, that of Marianne Bailey. Despite an income of over £50,000 a year, because it came from rental properties etc. it didn’t count. Nor does my wife’s PhD funding. And, sadly, nor does any income from self employment.
In the old days you just had to be above the poverty line, and if you weren’t then you could get a friend or family member to sponsor them. Unfortunately you can’t do that now – your only real option is to find £62,500 of savings (I think you need to have had this in her account for some time, several months at least), get a full time job, or get her over here with a full time job. This is unlikely to work- they were funny about letting my wife back in on her student visa that let her stay until February 2013, following the end of her course in July 2012 and our marriage in September 2012. They said at the airport her main reason for coming back was to be my wife, not a student. If you apply for a work visa of some kind then they’ll pick this up, and she’ll not get a job without one before applying.