Neither ball bearings nor caltrops indicate that the speed of a creature is physically penalized, but simply that a creature can choose to move at half speed to avoid its effects. Then we can treat each consideration separately.
First, ball bearings
As an action, you can pull these tiny metal balls out of their bags to cover a flat, square surface 10 feet apart. A creature moving through the covered area must make a successful throw or fall, sparing DC 10 dexterity. A creature moving in the mid-speed zone does not need to make backup.
Does the creature move at half speed in the area of the ball bearings? Then they are not affected.
Then, caltrops (emphasis me):
As an action, you can spread a bag of caltrops to cover a square surface 5 feet apart. Any creature that enters the area must either make a DC 15 Dexterity save roll or stop moving that turn and suffer a piercing damage. Taking this damage reduces the creature's walking speed by 10 feet until the creature regains at least 1 life. A creature moving in the mid-speed zone does not need to make backup.
Does the creature move in the caltrops area at half speed? Then they are not affected.
An area covered with both ball bearings and caltrops is no different. Does the creature move in the area at half the speed? Then they are not affected.
Note that if the creature chooses to move more than half of its velocity on the combined surface, it will be forced to make both save throws, one against the ball bearings and one against the caltrops, which may suffer damage. one or the other effect or both. combined.