B is for base. Without a base resistor, there is nothing limiting the current drawn from the Arduino pin. You should limit the base current to something around, say, 1/10th or 1/20th the current which is drawn by the LED strip. This is the energy "tax" for using a bipolar transistor. You might get away with less. The "Hfe" of the tranasistor can be found in the datasheet. An Hfe of 100 technically means that the transistor could switch up to 100x the base current; and there are transistors that go even higher. But due to variation between devices and other stuff I never bothered to learn, myself, I understand it is common practice to simply shoot for a base current of 1/10th the current of the load, when using a BJT as a switch.
You could alternatively use N channel MOSFETS. A gate resistor is often used to prevent ringing, and to prevent temporary high draw from the Arduino while charging the gate. But it can often be omitted. OTOH, a pulldown resistor on the gate would be desirable, but not strictly mandatory, as well. So while it is totally possible to use an NFET driven directly by the Arduino without any additional resistors, it is common to use a gate resistor AND a pulldown resistor for a FET in this type of usage. You can decide if you would need those, yourself. I often drive (small!) FETs directly from a micro pin but there are often minor annoyances that can occur when leaving out the pulldown resistor... e.g., the LED strip might be energized before the Arduino starts to do what it is supposed to, and the LED strips might temporarily blink on when you first plug in the power because the gate of the FET happens to be floating high. Omitting a pulldown resistor on a FET gate can also leave the FET much more susceptible to death by static electricity when it's not plugged in. Common values for something like this might be 10R for the series resistor, 100K for the pulldown.
The max current one of your Arduino pins is probably around 25mA, plus or minus 10mA. So your LED strips should be max of maybe 250-500mA draw if you want to switch them with single BJT. But don't use this 25mA max as what you will get without any base resistor. If you don't limit the current with a resistor, the pin will suffer internal voltage drop and heating and will not necessarily work as you think it will.
Ohms law, voltage/resistance = current. Voltage from your Arduino is 5V, minus the drop across the B-E junction, which you can fudge at 0.6V. So 4.4V. Figure the current you need and you get your resistance. 4.4V/desired base current in amps = resistance in ohms.