If I lived on my own for about 7 months of 2020 and paid my own bills for those 7 months, should my parents claim me as a dependent? Single full-time student.

Possibly.  You didn't mention your age which has a significant bearing on the situation.  I assume you are under age 24.  If so here are the criteria for you to be claimed as a qualifying child.  Rule number 4 below is also applicable here.  A case could be made that you provided over 1/2 of your support.  In this link you will find worksheet 2 to help you figure that answer.

Total support includes amounts spent to provide food, lodging, clothing, education, medical and dental care, recreation, transportation, and similar necessities. Generally, the amount of an item of support is the amount of the expense incurred in providing that item. For lodging, the amount of support is the fair rental value of the lodging. 

If you provided over 1/2 of this total support no matter how many other sources provided the rest, then you would not be a dependent. Scholarships for example would be support provided by someone else, not you.  

Of note as well is any time spent away at school is time counted as living with parents so that satisfies rule 3 below.

1. The child must be your son, daughter, stepchild, foster child, brother, sister, half brother, half sister, stepbrother, stepsister, or a descendant of any of them.

2. The child must be (a) under age 19 at the end of the year and younger than you (or your spouse if filing jointly), (b) under age 24 at the end of the year, a student, and younger than you (or your spouse if filing jointly), or (c) any age if permanently and totally disabled.

3. The child must have lived with you for more than half of the year.

4. The child must not have provided more than half of his or her own support for the year.

5. The child must not be filing a joint return for the year (unless that joint return is filed only to claim a refund of withheld income tax or estimated tax paid).