It's much harder to get rid of Combined Chlorine in a hot tub or an indoor pool since they are not usually exposed to sunlight which helps break them down. Also, a hot tub has a much higher bather load than a pool due to the small volume of water. That means that organics tend to overwhelm chlorine faster and more combined chlorine forms.
First of all, you should have at least some Cyanuric Acid (CYA) in the water or else you will be overdosing with chlorine. I suggest using Dichlor for about a week to get to a CYA level of around 20 ppm. After that you can use bleach by dosing to around 4 ppm Free Chlorine (FC). You may need to add some chlorine every day after you get out of the tub if you are using it regularly.
To keep the CCs lower and to lessen your chlorine usage, you can use non-chlorine shock, potassium monopersulfate (MPS), and can use a little each day after you get out of the tub -- probably around 1 teaspoon. Note, however, that MPS will register as Combined Chlorine in the chlorine test, but you won't create any true combined chlorine if you are using MPS since MPS will oxidize organics (and ammonia) before chlorine gets a chance to.
0.4 ppm CC is not bad so if you want to just use a regimen of shocking with chlorine (bleach) weekly instead of using MPS, then that's OK. It's really up to you. I recently used some MPS in my pool to get rid of an oil film that didn't go away with scum balls nor enzymes. I could have shocked with chlorine, but since my wife was using the pool every day I didn't want to have to wait for the chlorine level to drop so I used MPS. It worked great -- it's very effective, but not cheap, but for a hot tub you use less than you would for a pool (though it's not proportional).
On a separate note, if you find the pH to rise in your hot tub, then you can lower the TA level to reduce that problem. Lowering the TA to around 70 is usually enough though you could lower it even to 50 if necessary (assuming you have a fiberglass tub and not plaster nor any tile with exposed grout). Using bleach is pH neutral when accounting for chlorine usage, but the aeration in a hot tub drives a lot of carbon dioxide out of the water and that makes the pH rise. Keeping the TA lower reduces this effect since TA mostly measures the amount of carbonation in the water (pools and spas are intentionally over-carbonated to provide a pH buffer and, for plaster pools along with calcium hardness, for calcium carbonate saturation).
Richard
