I think the question you need to ask is how good will my LOR be if I've only known the professor for a semester. When I applied to grad school the first time, I had been in 3 classes with a professor, and he still asked for a list of my accomplishments and extracurriculars because his recommendation would sound terrible not knowing anything about me other than that I did well in his class. It's very important to do well in a class, but the recommendation really should fill out who you are as a person, especially in applying to a professional degree like OT. I would visit with her in office hours as much as possible while you can.
As to the actual asking...I told a professor that I felt terrible befriending him just to get a LOR, and that I really respected him and wanted to get to know him regardless. He told me that it's part of the job, and that all good professors expect to do it. If it's a big name professor, then you might have some trouble (if it's worth the trouble, then it will be tough to get), but in general, if they don't want to do a LOR when you're a good student, that means they're a jerk and shouldn't be teaching. LOR's are part of the job, and most good teachers want to help you out.
