Depends what type of DSMB you've got.
You can get ones with an open or tapered bottom, through which you can either inflate by purging your octo into it, holding it so it captures your exhaled breaths above your second stage, or use an air-gun (if you have one fitted).
Or you can get them with one-way valves fitted (sounds more like the one you have), through which you can inflate by either plugging them on to your BCD whip (a real faff) or by taking out your reg and blowing into it.
My mate has one like this, made by Halcyon, and in the Red Sea in December when it was necessary to launch one DSMB per buddy team prior to doing our 5m stop and surfacing he perfected his launch. He would take a big breath and then take out his reg and blow into his DSMB, at the same time pulling on his shoulder dump valve on his BCD to vent what little air he had inside. This had the effect that his buoyancy remained much the same, and he would then replace his reg, take about big breath, remove his reg and then blow into his DSMB again before replacing his reg and letting the DSMB head off to the surface on a free-spinning reel. These two breaths, from a depth of about 8-9m, meant the DSMB was 90% full on the surface. Might not work for everyone, but certainly worked for him.
I've got a smaller Scubapro DSMB with a tapered bottom, and I can adequately fill that by holding it near my second stage and letting it capture exhaled breaths. Two big exhales and I can send it up from 6-7m and it is 85-90% full at the surface. Again, works for me.
Main thing, whether you are using a reel or a spool, is practice, practice, practice. Can't count the number of people I have seen rocketing to the surface grimly holding on to their DSMBs, including the Course Director who thought it was a good idea to clip his reel on his to wing while he launched the DSMB.
I think some divers forget the amount of lift these things can generate.
Mark