Make sure you tune every string to the tuner individually and do it in a cycle over and over until you go all the way through without changes. Recheck after a while. My mando usually takes about 3 cycles. The first time through, each successive string is adding quite a bit of tension which has the effect of relieving tension on the strings already tuned. The second time through I often find strings over a half interval (G measures a slightly too sharp f#, for example) out of tune. It will need tuning after playing a bit, maybe again after a couple of days and then it stays in tune pretty well (a little tweak here and there). Yours may be different of course. As far as bridge adjustment goes, that is usually a tweak that you wouldn't notice in a jam or playing on the first few frets. If the bridge is off .25" (quite a bit) the 7th fret will only be off by about .075" or about 1/8 of an interval; far less than what you get from purposeful bending and more accurate than a lot of fiddlers that sound pretty good.
"First you master your instrument, then you master the music, then you forget about all that ... and just play"
Charlie "Bird" Parker