I always pull the string (gently) vertically at the 12 fret until it meets resistance, play the string to see if it is flat, and repeat until the string relaxes out of tune very slowly. It only requires a few repetitions. Then I tune the string up a semitone and play the string until it relaxes into the correct note, rinse and repeat until the note stabilizes.
I do this for each string and takes about 30 - 40 minutes, depending on whether it is the 6 string or 7 string. The strings will continue to stabilize over the next two days, but only need retuning once a day.
I haven't had any neck bowing in any of my guitars, or problems with the bridge. It is important, though, to not keep pulling the string when you feel it resist. A new string will be in danger of breaking, and going past that point could potentially hurt the guitar over time if you do that every time, but the guitar is much stronger than your strings. I don't know the effects on very thin tops, however, as I've never owned a doubletop or lattice braced guitar.
198x Yamaha G 55-1 (fretless)
1999 Yairi CY110
2013 Milagro MRS7 7 string