I would take a few measurements before anything else.
Begin by slugging the bore. Take a pure lead ball slightly larger than the grooves (a little undersized is fine, just smash it slightly with a hammer), grease it, and force it down the bore from the muzzle. (I like to start it with a wood/leather/plastic mallet, then push it through with a wooden dowel). Pay attention to the last bit where the barrel is screwed into the frame. It's not unusual for the bore to be a few thousandths smaller there, and that "thread choke" can ruin accuracy, especially with lead bullets. Then measure the slug to get groove diameter.
Next measure the throats. The best way to do this is with pin gauges in .001 increments. You can buy a big set to cover everything for a hundred bucks or so, or you could cover the .38/.357 bases with six or so (.354 to .359) for maybe twenty bucks. You also can slug them like you did the bore, if you happen to have more lead balls and don't mind the work.
In my experience, these measurements will usually explain any accuracy problems. If "thread choke" is the issue, the bore can be lapped - either by hand or with fire lapping - to remove the constriction. If the throats are smaller than the bore, they can be reamed to .0005 or .001 larger. If the throats are much larger than the bore - more than .003 or so - then you are pretty much hosed, though Taurus might be persuaded to exchange the gun.
There are a few other things that can explain poor accuracy, but they tend to be more rare, more difficult to diagnose, or both.