A bit is stuck in the chuck of my Bosch drill

Drill is illustrated with a keyed chuck but in most cases if the drill is reversible there is a L/H thread machine screw accessible between the jaws when the chuck is wide open. This screw must be removed first.
A keyed chuck is removed by fitting the key and striking it sharply with a hammer in the normal direction of rotation.

Removing a keyless chuck can be difficult - the principle is the same but clamping something onto it tight enough to shock it with a hammer usually causes damage. The chuck of a reversible drill can clamped in a vice and the drill operated (carefully) in reverse sometimes does the trick.
Ideally what is needed is something like a few inches of 10mm hexagon bar bent at a right angle - locked into the chuck it would allow a hammer strike without causing damage.

I would put the drill in reverse and hold the "chuck" and very slowly and carefully press the trigger lightly. This should bring the clamping device back where you can see it.

Here's a link to an exploded view:
Bosch PSB 600 2 0603338003 Spare Parts

If you need more help - you should contact Bosch directly:
Contact Bosch

manufacturer can supply you with a new chuck. Mounting bolt is typically through the front opening into the back portion near the drive assembly

Can not see what model you have. Is it a keyless chuck or an SDS chuck? With a keyless chuck hold the machine in a vice by the drill bit. now tap the chuck with a hammer or pin punch & hammer. DONOT hit the chuck on the jaws gut on the rim around them. I have had success using this method. If it is an SDS type chuck pull the chuck cap up as far as possible along the bit them if there are any ring springs you will have to try remove them then slide the sleeve up the bit, now you should be able to remove any steel balls. If the bit does not come out now hold bit in vice as before and tap on tool holder.

if you open chuck all the way the drill bit should just fall out

You have wound the threaded section of the jaws fast the thread in the case so sorry the chuck is broken as the teeth will be damaged. Best replace it with a new chuck

while holding the drill like a gun, hold the lock button REALLY tight and pull the black part to the right really hard. this will unlock the chuck and if you keep twisting the black part to the right it will loosen it enough so that you can remove it

you can't drill counterclockwise the bits are setup to drill clockwise and the chuck would become loose. try using two wrenches to free up the chuck then spray a little wd40 in it it is just bound up

These units have only been out for a short while and most are on warranty. Take it to a Bosch Service center in your area and they will replace the front of the unit. Unfortunatly this is a problem with this type of unit. The bit will deform slightly from the impacting action and lock itself in the chuck.