1. Talc the tube well. It really helps with the last bit.
2. Try thinner rim tape as has been suggested.
3. If all else fails, fit the tyre without the tube using tyre levers a couple of times. This will stretch the bead a little. Then try again with the tube.
4. Don't worry too much about changing a tube on the road. Many tyres are tight when new (Vredestein Fortezzas are a struggle on most rims) but can easily be fitted and removed without the aid of tools once they've been sitting, inflated, on a rim for a couple of weeks.
EDIT: I see mrcharly has already suggested 3 and 4, so I'm completely redundant here