if you don't move then it depends on the parity of the sum of your stars in previous stages
odd: lone rider
even: merchant

e.g. if you get 5 stars in stage 1 and 2 stars in stage 2 then you get lone rider, if you get 1 star in both stages you get merchant

you can force a boss by flying to the top of the screen or to the bottom right of the screen before islay shows up
former makes lone rider appear, latter makes merchant appear

dang yea no wonder i couldn't figure it out thanks for the explanation