I got it within two resets (one for set of tyrannical +15 and the other for fortified). In my case, having good ilvl from PvP (basically full set of 270 items or something, with 4 set bonus) kinda carried me. I also think most people, even if they are pve players, recognise high arena ratings as a measure of skill so it was pretty easy for me to get into groups. First I made my own groups, but then I started to need specific dungeons and to my surprise I was invited to +15 pretty fast, even though my score was still low, so it must have been the gear (high ilvl with low m+ score must indicate either 2100+ PvP rating or mythic raiding so people were inviting me I guess).
However without PvP gear (or mythic raiding) I think it would be a much longer process, probably like 6 lockouts, or even more. I can see why someone would just throw some gold on boosters to make it faster, if they really wanted KSM. And if you do a lot of aide content, like WQs, callings, professions, old raids etc. then gold isn't really an issue.