Last summer I planted 3 varieties of bush beans (green, yellow and purple), in rows mixing all the seeds up, so all three varieties were randomly mixed up in the rows. (hoping for a cross) I had quite a lot of bumblebee action and think I managed to get some crosses.

When I harvested the dry seeds, many had unusual markings and colors, not like markings or colors of the parent beans I planted, is this a sign of successful cross?

I cant wait to plant these out next season to see the results.

Possibly but you can't know for sure until they grow out. And honestly even then it may not be clear since so many of the characteristics other than color are recessive.

The bean bloom form makes active crossing difficult (but not impossible) and in most cases the bloom is already pollinated before it even opens and is accessible to insect activity.

For growing out I'd actively select the most uniquely marked seeds only.

Dave