I used to have pwd on phone, computer, tablet, etc. My gf had no problem with it. She asked me every time.
You're not being irrational and she shouldn't be suspicious. I guess some girls/women are just more nosy than others. It's not a trust issue. It's simple respect and "give me some space".
It's up to you to draw the line. She'll understand... after going apeshit over it of course.
