It's hard to say without a picture. The mental image is going either way. Do you have an example of what the complete product looks like?
Though, just wearing a bra to cover your top can be considered a little slutty, because it really exposes you. One might say, how is this different to for example wearing one at the beach? It's different because of time and place. At the beach everyone is wearing one and the pupose for going to the beach leads to it. Wearing only a bra to cover your top at the Gym, instantly makes you the focus of male attention and seperates you from most of the other girls in there. It can be considered attention seeking by some people. Besides, you don't need to catch sunlight at the Gym, something less revealing maybe in better taste.
Don't cry, don't regret and don't blame
Weak find the whip, willing find freedom
Towards the sun, carry your name
In warm hands you are given
Ask the wind for the way
Uncertainty's gone, your path will unravel
Accept all as it is and do not blame
God or the Devil
~Born to Live - Mavrik~