Here's what I would do: Keep your .38 in a high quality holster (like a Galco), either in your nightstand or on your person at all times (except when sleeping, of course). If an intruder appears in the middle of the night when you're not dressed, and you're pressed for time, just leave that .38 alone and go for the shotgun. (You can go back and get that .38 if necessary, although it probably won't be). OTOH, if the intruder appears in the day, you're appropriately dressed, and you have a little time, then grab that holstered .38 (after getting your shotgun first) and stick it in your pocket. Most likely you won't need it, but it's always wise to have a backup that you can access (draw) quickly.
It's also wise to take a tactical class that specializes in training for the type of scenarios we're discussing.
(Btw, the 158 gr. SWCHP +P "FBI load" is a very potent round for the .38 spl, if your piece can handle the high pressures).