If you are not trailer trash, but your straps keep falling off, it is because your bra does not fit you. Go get a free fitting at a wide variety of stores. A good fitting bra will flatter your body and improve your self image.
On a side note, I personally have a problem wearing a shirt that clearly shows my bra. I know everyone knows women wear bras so it shouldn't be a big deal, but I think it looks really tacky to wear a regular bra with lets say a racer back tank top. I have this neat little contraption that brings my straps together to hide nicely under the shirt. I also have a bra that the straps adjust and can cross, allowing them to hide. There are tons of website that sell bra straps so if they do show, they can be pretty, and I have 'clear' straps that you can see, but does look better than something else. I have a strapless bra which is next to impossible for me to put on by myself (I know that sounds horrible, but when your breasts are 34F, it is difficult) and of course the boobs look different when in a bra like that. But if I can make that kind of effort to look decent when I am in public, I expect the smaller breasted woman to do the same.
If it is going to be done, it can be done a little better - perhaps deciding on a bra that complements the shirt. Don't get me wrong, I don't mind seeing a little bra strap peaking out. I have a bigger issue with wearing lets say a halter top or a backless shirt and a normal bra, wearing one of those super cute trendy shirts that wearing a 'normal' bra is difficult - but it should be worn with taste. I bought one and went through hell to get the bra to be concealed or wore a little cardigan over it. If you are buying something 'cute' like that, don't make it un-cute by destroying how you look in it.