Why are bruises not lethal?
blood clots inside the body have an unfortunate tendency to get into the bloodstream and cause blockages, leading to severe problems such as strokes or heart attacks


This statement is primarily true only for blood clots within blood vessels, especially in the veins. When you are talking about bruising, you are talking about clots outside of the vasculature.

When a blood clot occurs in an artery, it can block that artery or break off, flow downstream, and block some smaller distal vessel. These events are most severe when they affect crucial organs like the brain and heart ("stroke" or "heart attack"), though of course any organ can be damaged in this way. However, blood clots in arteries can't ever directly affect a tissue that is not distal from where the clot starts, because they can never pass through capillaries or travel backward.

When a blood clot occurs in a vein and is dislodged, it can follow the increasingly larger venous system back to the heart, where it can cause a pulmonary embolism (blockage in the lungs) or, via a patent foramen ovale, travel to the left-side circulation and end up anywhere, including the coronary arteries or blood vessels of the brain. Similarly, clots that form in the venous return from the lungs to the heart or in the left side of the heart itself can travel anywhere (except the lungs) and create a blockage.

For a clot outside the vasculature, for it to have an effect somewhere else systemically it must re-enter the vasculature. This is simply not possible in most situations, because the vessels involved are very small, and during bleeding the blood is flowing out of vessels: there is no pressure gradient to push the clot back into the vessels.

In more severe cases of injury where major vessels are involved, clotting in those major vessels can indeed be a problem, but not for common occurrences of bruising.

(see also @anongoodnurse's answer that contains a good clarification of what exactly a bruise is, as well as how there are risks from very serious bruises but not the same way the original question implied)