Even with off-camera flashes, it's not uncommon to modify them in some way, especially diffusing them. For example, you might have some flash mounted on top of your camera with a simple translucent white diffuser to soften the light. Or perhaps you want to take the so-called "strobist" approach and mount that small flash on a tripod and modify it some other way, for example fire it into an umbrella or a softbox. Unless you're trying to narrow the focus of the light and increase its intensity using an attachment like a snoot, then any diffusion modifier is going to decrease your overall light output since the goal is to soften it.
It sounds like for your purposes, firing a flash or full-sized strobe (or two) into an umbrella and thus bouncing the light onto your model, will probably be the easiest and most cost effective. You'll likely need multiple flashes if you want to take the "strobist" approach of using camera-mounted hot-shoe flashes. Otherwise a full-sized studio strobe with a battery pack or a professional portable strobe would be excellent. If cost is an issue, or if this is a one-time shoot, then you might consider renting a pro portable setup. If you're going to be doing this a lot in the future and cost is an issue then look into the strobist thing. If cost is not an issue and you'll be doing this a lot in the future then I would strongly suggest shelling out for pro gear. The other advantage of pro gear is that the output is high enough that you can control your light really well even in broad daylight.
Two shooting considerations to keep in mind: 1) You want to match the color temp of the flash light to the ambient/natural color temp. So if there's a sunset at dusk showering everything in warm light, you would probably want to place a warm-colored gel in front of the flash. Conversely if the ambient light is cool, you might want to use a cool-colored gel on the flash. 2) If you light your subject too brightly then the contrast may end up being too high between subject and background and your field will turn out black. Make sure you understand the dynamic range of your camera's sensor or film well and its relation to your flash power. If the ambient and flash meter readings are too far apart then you probably won't make the shot (painting with light, i.e. exposing for ambient and then flashing the subject doesn't work well with people for the obvious reason that they move).