Equisheim, Riquiwihr and Ribeauville - how to get to?

It is difficult, just about everywhere, to link multiple small towns on a single day. Sometimes you get lucky and two places you want to visit are on the same bus line, in which case it's just a question of how frequently the buses run. Otherwise, you end up having to travel back to the nearest larger town and head out again. Doing that, it's quite difficult to see more than two towns in one day, however small they may be.

Renting a car will be vastly cheaper than hiring a private driver for the entire day. Alternatively, it might be possible to travel the first leg (from Colmar will be easier than from Strasbourg, I think) by public bus, and perhaps the final leg back to Colmar as well, then use separate taxis for the interim hops. I believe the distances are short. However, I have never attempted that anywhere, much less in Alsace, and I don't know how many taxis are floating around. Those are tiny towns, and most people travel by car.

You can use Rome2Rio.com to explore bus availability in that area. However, you must ignore the fares, travel times, and frequencies displayed on that website. Just use it to drill down to find the names of the bus companies you need, and go to their websites to find actual schedules. The fares will be inconsequential, so you don't need to worry about those.

Edited to add links found on Rome2Rio.com:

Fluo buses (#208 to Eguisheim, #106 to Riquewihr, #109 to Ribeauville)
Taxi La Ligne Verte
Absolu Taxi Services

Riquewihr and Ribeauville are fairly close together but farther from Colmar than Eguisheim. You can save some money by taking a bus to and/or from one of the first two.

We spent a week in Riquewihr w/o a car, and as Acraven said, going to multiple villages by bus in a single day was difficult. On the other hand, we walked from Riquewihr to Ribeauville, stopping at another village on the way. Then I believe we took a bus back. Given that you'll be coming from Colmar or Strasbourg, I think a car would make sense.

You will get to see more of what you want to see in this area with a rented car.

Edit to add: I realize now that you are trying to see all these places in one day. I guess you can just about do a drive by of them all in a day but I don’ know how much time you will actually spend seeing/enjoying them. Without a car and with one day, you could probably visit one village out-and-back from colmar.

Could I visit all of these in 3 days from Colmar taking the bus?

I assume you could. Follow my link to the bus website and check the schedules. It might be a problem if one of the three days is a Sunday or holiday, though.

I have driven in that area and having a rental car will also allow you to see other cute, quaint towns on the outskirts of Colmar. It's very easy driving in that area and there are parking lots on the outskirts of each town. There is a Europcar location in Colmar.

There are more options for car rentals in Strasbourg, AFAIK there's only one rental agency in Colmar. You'll be able to visit more villages with a car. Best would be to train to Strasbourg, pick up a car, base in one of the villages for 2-3 nights and day trip into Colmar, then return to Strasbourg and drop the car. I stayed in Eguisheim and was well pleased with my choice.

Without a car, you'd need to stay in Colmar for buses to the villages. There are others worth seeing, Turckheim, Kayserberg . . . and sights like Haut-Kœnigsbourg and Monkey Mountain.

We took a high speed to Strasbourg from Pairs. After a dew days, we picked up a rental car and drove to our next base in the wine village of Riquewehr. Any of the wine villages would also be good choices.
The only place we did not care for in the area was Colmar where we spent a full day.

I like Colmar a great deal, but it definitely gets a lot of tourists. The very good Unterlinden Museum was nonetheless uncrowded during my summer 2017 visit. As always, most of the visitors were concentrated in a limited area of the town, so I had lots of streets all to myself.

I opted to take a day-trip to Selestat rather than one of the tiny villages. As advertised, Selestat is extremely untouristy.

A $100 is a bargain if you get to do what you want to do. We paid about €130 each for a full day wine tour with a couple of villages thrown in. It was excellent and what we wanted, but more than double the car rental.

We did visit a couple of other villages (we were based in Colmar) by taxi and bus, but it was not efficient. We had time (6 nights) so could afford to go slowly. On a return trip, I would base in Ribeauville and rent a car.