To the OP: your parents are married, correct? If not, note that most schools with good need-based financial aid require cooperation of both parents on financial aid forms, and will use both of their income and assets to determine financial aid.
As of today I agree. Bates does have courses in CS, but no dedicated major. That will be changing in the near future, however. Bates is in the early stages of designing and fundraising for a new CS major.
What level of Bright Futures award are you eligible for? I would put the Florida public universities as safeties and get those applications out asap.
Also look at Questbridge. They will assist with scholarships/FA.