Due to the nature of the mods and the level of configuration of them this may vary between setups. However, there is a faster way than waiting for the bees to simply give you enough silky comb.
With FTB Ultimate you have Twilight Forest installed. Down in the depths in their chests you can find a handy block called an Uncrafting Table. This little doodad allows you to craft, uncraft and repair many of the items in the game just using the recipe entries. However it can be configured to disallow certain things and will disallow some by default.
However I do not think this is one of them. Silky string can be made into string at a 3 to 1 ratio. So the uncrafting table will let you take a piece of string and uncraft it into 3 silkies. There are numerous ways to get string in the game from spiders, to mineshafts to uncrafting wool blocks. Certain configurations might even have things like a Cotton Plant.
Anywho. If the uncrafting table is not available to you or the recipes for string to silky are blocked, waiting for the bees to do their thing is the only other choice I am aware of.