There is no easy way to calculate this for liquids because the heat exchange will depend on whether there is any convection in the liquid or not. You can calculate the solution for the heat (conduction) equation for your geometry, but this may or may not give the right answer. The problem is a lot better defined for solids which can not convect.
The solution to the heat equation in cylindrical coordinates can be found in many physics books and scripts. It will neglect the bottom. There is another question that you need to consider: how homogeneous does the temperature have to be in the bootle? Unless the liquid is being stirred, there will be a significant gradient. If you look at the way chemists are doing their temperature dependent reactions, there is almost always some rather strong stirring or agitation going on, otherwise things may react differently in one part of their beakers than in another. You may want to stir, too.
The good news is that stirring simplifies the physical problem and it will, at least that's my gut feeling, reduce the time for the heating and the variation in the time it takes to get to the right temperature. The heat equation can then be reduced to the boundary, which is characterized by an effective area and an effective thermal resistance.
As a final comment: I would never leave the health of my baby to theoretical calculations. The only safe method is to measure the temperature.