graciela, glad you're enjoying the commute. Welcome to the ranks of the cycle commuters! You seem to have a well-reasoned out plan and route in place for getting to and from work.

As to your question, I'd say that once you're in the left hand turn lane, signal your intention to turn and stay positioned squarely in the middle and take the whole lane. If you move too far to one side of the turn lane or the other, you risk motorists trying to squeeze around you somehow, including once you enter the intersection. Signal your intention to turn and confidently take the lane.

It takes a little practice and experience to feel comfortable on the streets surrounded by quick-moving two-ton steel cages, so it may seem a little weird at first. OTOH, if you find you're really not comfortable there or feel unsafe, there's nothing wrong with your current strategy of dismounting and crossing.

Good luck and happy pedalling!