A pregnant woman with bleeding doesn’t fall under the rulings of hayth blood. So she doesn’t need to do ghusl after she clears. But what if she doesn’t feel comfortable not doing ghusl?

Ghusul (the ritual bath with the intention of purification from major ritual impurity) is a worship act. One cannot do a worship act in a way or time when we are not commanded to do it. So she cannot do that. She can, however, just take a regular shower without the intention of it being ghusl.