Bra sizing is really tricky, it varies so much for brand to brand and style to style. TBH if you want a properly fitting bra you need to learn to fit yourself properly. Some bra fitters are excellent but many, many more are worse than useless. The good one usually do it by eye, even if they do get a tape measure out for the form.
The band should provide the support not the straps, IME it's usually only women with self supporting breasts that can wear their 'true' band size and get sufficient support. For example, my breasts are anything but self supporting (think spaniels ears). I measure a 34 but if I wear anything bigger than a 30 the band rides up my back and my shoulders take the strain. A jobsworth bra fitter would put me in a 34, M&S would probably put me in a 38...
Bravissimo have good instructions on fitting, here.
It is handy to measure yourself to get a starting size, even though it'll only ever be a guide. I've copied this from one of my old posts [lazy]. How to measure:
First you measure the ribcage directly under the bust. That measurement is your band size, never add 4. That used to be right but the industry standard was changed years ago.
You calculate the cup size by the difference between the rib measurement and the bust measurement. 1 inch = one cup size.
So a band measurement of 34 and a bust measurement of 36 is a 34 B. But, that's just a guide, you may find that a 32 C, 34 B or a 36 A gives a better fit depending on the brand and style of bra. Some times you may need to go totally 'off piste' to get the right fit.
The same underwires are used in different cup sizes, the underwires in a 32 c, 34 B and a 36 A are all the same size. You MUST adjust the cup size if you adjust the band size.
Always try bras on at the loosest band setting, a 34 worn on it's tightest setting (when new) is a 32. The band will stretch with time and you need to be able to take it in as this happens. The band should be tight but you should be able to get two finger under it. Underwires should stand flat to your ribcage, if there's a gap the cup is too small. If there's wrinkling on the cup then it's too big.