Since I do not believe it has been mentioned yet, late October thru March is prime season in the Revillagigedos Islands (aka Socorros Islands) of Mexico. It is not colorful reefs but it is some of the best large animal diving there is, with hammerheads and 4-6 other types of sharks, tunas, and arguably the friendliest mantas and dolphins you will encounter anywhere. In November and December, there is a decent chance to see whalesharks, while in February and March, the humpback whales are around, altho seeing them underwater is still are very iffy proposition.
There are about 5 boats that do these islands and I've always heard good feedback on three of them: the Nautilus Explorer, the Solmar and the Rocio del Mar. I haven't heard much on the other two so I can't comment.
Myself, I've always gone on the Solmar V. The food is well above average in my opinion (but food is a very subjective thing) and their desserts are among the best I've had on liveaboards. And yes, they do have wine but you have to pay.
You will get 3-4 dives a day, but on a typical trip, you will get only about 18-19 dives - definitely not a lot of dives for the length of travel (you have to fly into San Jose de los Cabos in Mexico). That is one of the drawbacks, along with the 24-hour crossing each way from the mainland to the islands.
The Solmar has two single cabins - they are the size of a phone booth - but I find them more than adequate, if you can get one. As a single female traveler, your chances of getting one of these single cabins are not bad, considering that there are more single traveling males on these trips than there are single females. But, it is still a matter of luck and they will not guarantee you a single. It depends on the makeup of the remainder of the passengers.
The two single cabins that I mentioned are standard cabins. The cost for a standard cabin on the Solmar is $3200 + 11% tax. It is $3300 for a superior cabin but all of those are doubles and it is extremely unlikely that you will get one of those all to yourself unless you are willing to pay extra.
I suggest that you visit their website (do a search for Solmar V) and sign up for their e-newsletter. Sometimes they have really good specials. You can also look at their video reports from past trips and see if this diving appeals to you.
As far as colorful reefs, in my opinion, the best are in the Indo-Pacific, and the prettiest I have ever seen have been in (not in any particular order of ranking) Fiji, Indonesia, Malaysia, PNG, Thailand/Burma, and the Philippines. I have yet to go to the Red Sea so can't comment on them. Of those, I believe that the least inexpensive liveaboards will be in Thailand, Indonesia, and Philippines.
I also agree with Kevster that if maxing out on the number of dives a day is most important to you, you don't necessarily have to do liveaboards to get 5 or more dives a day. You can easily get 5 dives a day on nice colorful reefs at a lot of resorts in Indonesia, Malaysia and Philippines.