A typical heavy bag routine will look something like this,
Light bag round or shadow boxing to build up a light sweat and then stretch out lightly.
3 x 3-minute rounds, this is to work on your technique, throw combos, work your footwork, keep your head moving and hands up.
4 x 1-minute power boxing, all out power punches in these rounds.
5 x 30-second punch out drills, each drill should have one non-stop combo, thrown with full speed and power.
Shadow boxing and stretch out.
With a routine like that you work on skill, power and conditioning, do that and you wont go wrong but feel free to mix it up. Remember the better your technique is the better your workout will be so don't get sloppy and investing in a pair of boxing gloves will also help, your hand speed will increase much better.
Also you don't need gear to keep fit, there are other things that you can do as well like body weights and running.