Is there a way to hide the dashed line around a selection?

In Inkscape Preferences > Tools > Selector, you can change the selection cue to something else (I've never tried it, so not sure exactly what it is). Or you can not show anything at all, which sounds like what you want..

Can I ask why you want to hide it? Because it really can be very helpful. I guess I have no idea your skill level, so maybe you'll be fine. But if you're a new user, there may be something else you can do to solve your problem with the selection cue...if you want to share. If not, Inkscape Prefs is your solution.