"a bit of myself" is correct and usable in written English.
It can be used to refer to a small part or aspect of one's own personality or identity. Example: "I usually keep to myself, but I opened up to her and shared a bit of myself with her."
I show a bit of myself on the girl in the picture".
I think I always start with a bit of myself because I am not imaginative enough to get completely away.
Tom Hiddleston is a perfect Jonathan Pine – polite, calm, charming, confident but self-deprecating, a little mysterious, very English and astonishingly handsome (in many ways, he reminds me a bit of myself).
I recognized a bit of myself in each of the readers: our pride, our training, our love of fellow Marines, our internal conflicts regarding experiences and choices, and yes, our sour grapes at a system that at times failed to live up to the standards it demanded of us.
On one hand I have managed to maintain the attributes that I've selfishly relied on since my early twenties but I've also lost quite a bit of myself along the way.
Before I discovered the original carefree black girl, I saw a bit of myself reflected in the members of the girl bands of the nineties, Scary Spice and All Saints Shaznayy Lewis.
I think I have a bit of proving myself ahead of me".
"I'm going to have to go and do a bit of studying myself tonight".
"I do write quite a bit of poetry myself," he said, adding that he had found time to write some verse whilst travelling on the train during the leadership campaign.
I do a bit of running myself, or maybe I should call it jogging, so I had come in my running shoes, thinking I might join in.
"Having said that, I did a bit of calculation myself when the two teams were formulated, and Tom's team's average ranking position was 16 and ours was 18.
