Your illustration is for waht is called a Z-fold or Accordion fold, where each panel is the same size. On a Letterfold the third panel folds inward and tucks inside, so it needs to be smaller that the front and back panels. 3mm seems like a lot to me, but you shaoud really be asking the printer what they recommend.
Note, this has nothing to do with bleed, which is extra space around the outside of the layout.
What do I have to attend if I want to print it borderless?
Most digital printers do not print borderless. Inkjet proofers can, but for a quantity of 1000, you will have to print without bleeds, or print to an oversize stock then trim. Trimming will add cost to project. I would suggest designing to the paper size, this will not require trimming. Do not place graphic elements close to the edge. The obvious strip of the nonprinting buffer area is unslightly, so place elements into the interior of the page.
Depending on the design and whether color is used, 1000 pieces may well be more economical on a press than printing digitally. Trimming is certainly going to add some cost, but it should be pretty small and you'll probably be paying extra for the folding, anyway, so the trim may not add much at all.