I don't know what bows "Bjansen" made, but if it is a hill style bow you will have little curve in the form and therefore it won't be too thin IMO. But, I would suggest you line each side with 3" flat iron about 1/10th to 1/8" thick...running some bolts through it every 6"-8" or so...with some closer to the upper edge and some closer to the lower edge of the iron (alternating bolts from upper to lower to resist torque on the form)...and I imagine you would be ok.
It will add a lot of weight to the form, but it will also add a tremendous amount of strength.
The other option is to leave side to leave more on the base side than you leave on the airhose side. You don't want the base side to flex. If there is any flex, it is better to have it on the airhose side, as the airhose will compensate for minor deviations on that side without altering your final product. Meanwhile any flex on the base side (with the formica side) WILL show up in your bow. You don't want the later. Then if you have to, you could vertically mount a 2x4 or a U shaped angle iron on TOP of the airhose side (airhose side) running your "straps" to the 2x4 or U angle iron with the plywood top piece of the form (airhose side) being a spacer/filler between the 2x4 and the base form.