Any bit that you try - when she is first bitted - is going to cause her to "chomp and chew" until she gets used to having a foreign object in her mouth. Some don't do well or like stainless steel and do better with copper (when we bitted our western riding horses - we used "sweet iron" which then rusted - a good thing and many horses love it. They don't have sweet iron bits for driving horses or for minis), some don't. Part of the purpose of the bean or french link, imo, is to have them salivate and to chew a little - this actually encourages a soft jaw and resulting soft mouth. There is a difference between chomping & chewing, chewing litely/occasionally and gapping at the mouth.
Some "chomping and chewing" could be because it's either too small or too large in diameter -however you won't know that until she's worn it enough to get past the initial accepting phase. Hmm, how to better clarify that...
To get her used to it - she needs to wear it. I generally start mine while they are eating. I bridle them when I catch them and tie them up (they are tied by the collars they wear - in front of their own bucket). I am generally not too far away and will keep checking on the ones I have bridled while catching/feeding the rest. Thus far, I've never had any issues with them geting hung up or pulling the bridle off - but it is a possibility. They learn to move the bit around and that they can't spit it out while they are eating. I also bridle them while grooming - they learn to accept it and ignore it when nothing is happening to it. I lounge them while they wear it - with no lines hooked to it.
To get them used to pressure - after they've learned to turn and stop from halter/drivingt lines, I use the line/leadrope hooked to bit and halter at the same time. I flex them around to each side until they learn that it's ok and they don't root out or pull against the bit pressure, then I take the line around their haunches on the side opposite from where I'm standing and step back, slowly and gradually pulling. If I'm standing on the left side, the line runs from the right side of bit and around the haunches, behind the tail over the hocks to my hand. When I pull, as she gives to the bit - she'll tip her head to the right, then turn her head more fully to the right and then step around and follow the pull. I keep her coming right around until she completely faces me again... And praise her. Repeat several times. Then switch sides and again repeat. Several times. Since you've already started ground driving her in halter - you should then be able to step back and start ground driving with the bit/halter hookup and get similar/same responses. You just constantly keep working until she responds and keeps her mouth closed w/o rooting out against pressure. When this is going well - you switch the line to just the bit - and repeat with flexing, then flexing into turning around and then step in behind her to start driving her.
When she is accepting and going well, you start finessing your rein/line handling and what you want is to get quicker, more responsive gives or responses...
Not sure how long this will take - personally it's taken a long time with one of our ponies (a hotter model). She constantly "gapped" her mouth - everytime she felt pressure. She'd be fine for the flexing and the turning around - until you started ground driving her, then she'd root out and gape her mouth. But we didn't work more than 60 days at a time and didn't even always work more than 3 days a week dureing that time frame - so it took longer to get what I wanted. This spring she is finally "getting it". Her mouth isn't strapped shut and she's light and lovely. She started ground driving late in her yearling year, was ground driven during her 2nd year and ten again last year as a 3 yr old at which point she also was hooked to a drag (but was still ocassionally gapping at the mouth)...