I see nothing wrong with a sports bra and shorts, except that some motorists can be pertty obnoxious to women at time. And watch that sunburn. I like a littel more coverage, I wear t-top tanks a lot.
You are referring to "baggies"; the kind with a shorts layer over the lycra. Most places have them. REI, maybe this site, performance...
Note: I hope you are not wearing undies under your bike shorts. You should be commando, less blistering and chafing that way.
Irualn
2015 Liv Intrigue 2
Pro Mongoose Titanium Singlespeed
2012 Trek Madone 4.6 Compact SRAM