maybe its just me but i have never been embarrassed to daven anywhere or infront of anyone. im mostly ashamed to daven in front of HKBH himself because i feel so unworthy. but not people. i can care less. i see a bunch of people doing much weirder things like wearing pants below their underwear, playing loud obnoxious music on their ipod, or people asking for handouts at red lights, teens yelling in the streets screaming obscenities and they dont seem phased in the least! id be mortified if that was me! but u know what? nobody cares either. people go about their lives not really paying attention to what others do. ive davened on subways, bus stops, supermarket parking lots or where ever i am and the zman tefilla came. however i wouldnt necessarily say id feel as comfortable if i lived in north dakota. example.
when i was about 16 i was waiting in a bus terminal and was heading back to ny. mincha time came so i found a corner to daven in before my bus came and when i was finished with shmone esray a little boy asked me if i was a witch casting spells. i never saw it that way before but i guess thats what it looks like from a secular perspective. i just laughed and said yes would u like me to turn you into a frog? (no dont worry i didnt, i just explained to him that i was praying and he said “oh ok”) besides that curious little boy (this was not a jewish populated area so he probably never saw a jew before) most people dont care what you do in public. try one time to say tehillim somewhere. ull see no one will notice or even if they do they will only ask out of curiosity but never to make fun. heres an example of that. i was once saying tehillim on a bus and a black lady next to me asked me what i was saying and i said “psalms” and her response was “oh i say those too! i love them.” see its not as weird as you think. and definitely dont feel embaressed to daven infront of another jew! we ALL daven!!! and were not judging you. i get so much nachas when i see other women on the subway saying tehillim. i love it!