I did something similar myself with an SBM-20 soon after Fukushima.
If its to be mains powered, then one of those EMCO high voltage modules that Dick suggested would be ideal.
If its to be battery powered, the 12v at 100mA required quickly becomes rather a burden.
The SBM-20 has no real measurable operating current, its absolutely tiny.
So an extremely low power boost converter might be the answer, but it will require more work and complication to build.
I spent about a week developing my own +400v boost converter, and it draws about 900uA from a PP9 battery which lasts for about ten days.
After all that, these days, I run it continuously in the kitchen off a 9v wall pack, so in retrospect an EMCO module would have been a much simpler solution.
Gamma background in Melbourne Australia ranges from about 60 to 95 microsieverts per hour, and its up and down like yo-yo from hour to hour.