How many pulls with water did you do on the bark? More the better until it starts to become less concentrated in colour, then you know you've extracted most if the water solubles.

Heat helps but can extract water solubles cold aswell, it just probably take more water. Heat help solvents carry more. More heat means can fit more into same volume of solvent.

The choice of non polar solvent depends on many factors, such If you want to freeze precipitate then heptane or shellite/naptha. If you dont mind the extra steps of salting out, extracting with xylene or dlimonene would be the go.