Bringing the bike does not effect the true job: if you bring the whole bike, they'll just take the wheels off to true them anyway, but certainly won't care if you do.
Assuming you have traditional spokes & nipples, tires & tubes won't get in their way either.
When you're there, just tell them you're a big guy. Go ahead, tell them your weight. Tell them you've been having trouble with the wheel repeatedly going out of true. Ask if they think they should re-tension the whole wheel as you don't want to keep coming back. Even if you do come back, they should touch it up at no cost just to stand behind their truing job.