Assalamu alaikum - I need advice about starting to wear hijab around my dad

Assalamu alaikum, I'm 20 and this year I transferred colleges. At my new school I see so many sisters in hijab and it made me feel encouraged and safe - I wanted to do the same. I ordered a few khimars and abayas and started a little collection, but I keep putting off actually wearing them at home. My main problem is telling my dad. May Allah have mercy on my mother, she passed away over a year ago, so it's just me and my dad now. I honestly don't know how to bring up serious things with him - I get so shy and nervous talking about my feelings. I'm struggling to find the courage to say I want to wear hijab. Lately I've been living a sort of double life: I leave the house dressed casually, then park somewhere on the way and change in the backseat into an abaya and khimar before I go about my day. I feel happy and confident when I'm wearing it. But when I go out with my dad I don't wear it, and that makes me uncomfortable, so I try to avoid going out with him when I can. Sometimes I decide to keep it on and come home wearing it; he hasn't reacted badly, just a bit confused because I didn't leave the house like that, so he asks and I panic and say I was at the masjid. It's been almost two months and I don't know how to handle this. I feel silly for making it hard - it's not like I'm doing something wrong. Does anyone have any advice on how to talk to my dad about this? How can I explain gently that wearing hijab is important to me, without causing a big argument or feeling too embarrassed?