Greetings Romy! Welcome to the forum. I hope you will be a regular member here. It is a great place to talk to other ratty parents.
Congrats on your two new boys! You will fall in LOVE with Dobby and Panda if you have not already. Rats are simply the most incredible, intelligent and loving animals in the world. You are in for a wonderful experience with them. There is so much to learn about rats and I am sure you will learn more each day about their personalities and behaviors.
Be on the lookout for the day to come when you get nibble groomed! (When a rat has become fond of you and decides you are one of its pack, they will try to "groom" you, as they would another rat, usually on your fingernails or fingertips by gentle nibbling (this is not a biting thing at all, but a soft and affectionate gesture from the rat). Consider it a great honor to get nibble groomed or licked by one of your boys!
I would not worry at all about Dobby being shy. There always seems to be a brave adventurous rat and a shy one. It happens so often it seems! By the way, I love your rats' names. Dobby and Panda, marvelous!
Dobby will just need more time to come out of his shell and lose some of his shyness, but he may always be a bit more timid than his brother. However, it usually seems to be the case that the shy brother will follow the lead of his braver brother.
Dobby will see Panda enjoying interacting with you, taking treats from you and so forth and will learn from his brother that all is fine and he has nothing to fear from you. It just takes some time and patience, but it sounds like you are doing a great job with being gentle and taking baby steps with him. He will get to know the sound of your voice, your smell and learn that you are a safe place for him, not a scary or threatening one.
You also mentioned that Panda stole Dobby's treat. Aww, poor Dobby. His brother may very well be the big macho bratty brother, eh? Well, a good rule of thumb is that when you give treats, try to give each boy a treat at the same time. If one rat sees the other getting something, he will want the same thing right away, even trying to steal his sibling's treat to get his own share. So whenever I give my boys treats, so they they do not squabble over who got what and so forth, I give them a treat at the exact same time, one in each hand for each boy. Then they are both happy with their own treats and there is no "Hey! I want that!" stuff going on. Heh heh.
I have never personally had any issues with my boy rats trying to climb down off beds, etc, as I adopted my boys when they were babies and they naturally learned that the edges of their free play area (bed, couch, etc) were not good to go beyond. When one of them would sniff over the edge, I would just gently guide my hand alongside him to sort of steer him away from the edge. With all four of my boy ratties, it was just something my husband or I would do a few times when they were young (sort of steering them away from the edge of whatever play area we had them on) and it quickly turned into second nature for them to sort of just lose interest or just to naturally avoid getting too close to the edges of their play areas. Might not work for everyone but it has never been an issue for me.
I figure they probably end up thinking, "Hmm, I have lots of fun blankets and boxes and treats here in the middle of my playground, and there is nothing out there over the edge of my play area so I have no interest in it." Maybe? Rats, if you have not already learned from some research, are amazingly intelligent creatures. I think my boys just learned very quickly after a few initial (and very gentle) steers/nudges from my hand away from the edges of their play area that it was just not a cool place to go wandering past. It is probably a combination of factors.
Rats also have a healthy sense of self preservation and they do not tend to be the kind of critter that will go jumping off an edge of an area into unknown space and risk the possibility of falling! I know some people have had rats that just love to climb down the side of a bed but my boys have never been like that.
An open space like your bed, especially with a large towel or blanket crumpled up on it for them to crawl under and "tunnel" through is a great time for rats. They love cloth, blankets, towels and just about anything they can play under or over, and tunnel through. Always a hit. And yes, of course cardboard boxes with entry and exit doors cut out of them are always fun too.
Hope we get to see some pictures of your boys eventually! You are in the Netherlands, wow! Greetings from the U.S!