The easiest way I found to charge the batteries was to get a general purpose charger for NiMh batteries from the local hobby store, like the one shown on the left. 

The charger shown here is from Conrad Electric (Voltcraft 115/230V 50-60 MW66168V Schnell-Ladegeraet for Europe) and can charge 2, 4, 6, 8, or 10 batteries at once, given you have the proper adapter and a holder for your batteries.  You can set how many batteries you want to charge with the small yellow dial. 

The 10x AA battery holder works perfectly for this and all you need to do is make an adapter with a 9V battery clip and the 5.5 mm round plug.     Be careful to make sure the polarity is right when you make the connections.    The + on the 9V battery clip is the serrated crown and the + on the female connector is the center pole. 

The charger is only  14.95 Euro and comes with alligator clips and a RC adapter.  Since this charger can charge all 10 at once, it is a great ease and convenience  not having to remove batteries from the pack and charge the batteries in batches since  typical battery chargers only hold 2 or 4 AA's at once.

Recharging all 10 at one time ensures that your pack will always be ready to go when you are ready to ride.

You can charge all 10 batteries at once in the water bottle with a homemade female-female   connector.   It adapts the male adapter of the Voltcraft charger with the male connector of the battery pack.  You will need two 5.5 x 2.1 female connectors, some wire and some heat shrink tubing.   Conrad has these connectors (Conrad 732770-62).  Soldering the small female connectors is not an easy job.  The connector is really easy to melt with the soldering iron.

I recommend you modify the RC adapter, with the white connector, that comes with the charger.   This is easier than soldering together the sensitive female-female connector shown above, but you have to cut the RC adapter that comes with the charger.  The easiest connector to solder is the female power connector used in the Tubelight, since it has larger terminals and you do not risk melting the plastic of the terminal like you do with the female connectors above. 

Cut the RC adapter halfway up the cable.   This way you can solder on a male connector to the other end if you do end up needing the RC adapter.

Strip 3-4 mm of insulation from the ends and tin the exposed copper wire with solder.

Assemble shrink tubing (3/32" diameter)  over each wire.    Assemble a larger diameter piece of shrink tubing over the connector.  

Solder the connector, taking care to maintain the polarity.   The wire with the white strip is positive and gets soldered to the center pole.  

Slide the small pieces of shrink tubing over the terminals and shrink it on.  

Slide the larger diameter shrink tubing over the connector and shrink it on. 

To make a more professional looking connector, you can use the Voltcraft RC power connector but with a.5 x 2.1 female connector.   The instructions are below for making this connector. 

Charging battery pack in the water bottle or battery pack  with the Voltcraft recharger.

Making a professional looking adapter with the Voltcraft RC connector and a 5.5 x 2.1 female connector

The RC connector that comes with the Voltcraft charger can be used to make a power adapter for a 5.5x2.1 mm connector.   Cut off the white connector as show left.

The "+" wire is the one with the "white stripe".   Cut the other wire 3-4 mm shorter than the white wire.   This is to balance   the length in the soldered condition on the connector.   Strip the "+" lead about 2 mm and the other lead about 3 mm. 

The "+" gets attached to the center terminal of the connector.  

The "-" gets attached to the outside of the terminal.  

Twist the wire ends together.

Pre tin the leads with solder.

Mount the connector in something so that it is stable while soldering.  

Apply solder and melt into the center connector.  Be careful of how much heat and time the tip is on the connector.   There is a plastic insulator between the inside and outside.   Too much heat can melt and damage the connector. 

Pre tin with solder the other connector below the hole in the lead.

Assemble the plastic threaded housing over the wire.  Assemble shrink tubing for insulation over the two leads.  

The shorter lead (-)  which will be soldered to the  long connection and needs shrink tubing to be a bit larger in diameter. 

The longer lead (-) will be soldered to the center connection.   The shrink tubing should be large enough to fit over the diameter of the center connector. 

Heat up the center connector and stick the pre tinned lead in the molten solder.  Let cool.

Slip shrink tubing over the connection.

Solder the "-" lead to the long terminal. 

Bend one side of the connector over and crimp.

Bend the other side of the connector over and crimp.

Slip shrink tubing over the connection.

Shrink the tubing over the joints to provide insulation.

Assemble the threaded plastic housing.