That's good that your new baby beardie eats so much! I got a 3.5 month old beardie and the first few days he refused to eat. Now he eats a few crickets a couple times a day and prefers greens and raspberries over the crickets & RepCal pellets.
And some beardies do have a greater appetite than others. I read that someone can go through about 60 - 75 crickets a day. Mine is a really picky eater and only goes through 10 crickets a day but attacks the greens, veggies, and fruits like there's no tomorrow! I don't understand why, since he's 4 months old and they usually like the crickets more.
Also, with the bath - you can start whenever you want. I started when my beardie was 3.5 months old (2 weeks after I bought him). Make sure the water is warm to the touch. If it's hot, it might overheat and if it's too cold, your beardie will feel very cold to the touch. Make sure the water is at chest level and keep an eye on him that he doesn't drown. a 10-15 minute soak once a week should be sufficient.
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0.0.1 Bearded Dragon (Cookie Monster)
1.0.0 Crested Gecko (Vas-D)
0.0.2 Fire Bellied Toads (Norman & Forman)
0.0.2 Goldfish (Lenny & Carl)
1.0.0 Black Lab / Pit Bull (Mikey)