A fresh, nearly empty bobbin.
Plenty of people complain they can't get a lot on their spinning wheel's bobbins. Bobbins come in all sizes, as does yarn, but there are a few things you can do about it. The most important is to wind on as evenly as possible. A mechanical level winder, like the Woolee Winder, is one way but you can't get one for every wheel and they are not cheap. The hooks or slider on your flyer can do a lot if you know how and remember to stop and adjust them often. Yes, you have to remember to do it, and it's a major pain for fat yarn because it fills up the bobbin so quickly. But for fine yarn there is little excuse but laziness. And it will make your life easier later.
Before I get to how, I want to explain why it's worth going through all this trouble. The more evenly the yarn is wound on the bobbin, the easier it is to get it off. First, huge mountains and valleys of yarn tend to slide around. A loop of yarn that falls from a tall bit to an empty space on the bobbin is no longer under tension. At best, it will relax and start to twist on itself and take up more space as it puffs out. This means less room for more yarn. At worst, it will snarl and tangle and make a mess that is not at all improved by adding more layers of yarn over it.
Second, mountains and valleys make the diameter of your yarn package change dramatically. This means the bobbin has to turn faster or slower while you are getting the yarn off it to keep it coming at the same rate. If you suddenly go from fast to slow, your yarn usually starts winding backwards on the bobbin in an annoying and unattractive fashion. Sometimes it will just puddle on the floor because it has nowhere to go. Move from slow to fast and if the bobbin can't react quickly enough your yarn might break.
Your spinning wheel has either hooks or a slider to control where the yarn is wound on the bobbin. If you have a slider, you can move it any amount you like, which is good. If you have hooks, you can only move to the next hook. If you have two rows of hooks, see if they are offset so you can move from one side to the other to get a shorter distance. If you have two rows of hooks but they are not on the same side of the flyer (one set on the top of one arm and one on the bottom of the other arm) it might be worth it to move one set to the other side or install some new ones. Yes, wheel modification is possible if you aren't too afraid to try it. Always remember that the person who designed your wheel is much more likely to be an experienced mechanic than an experienced spinner. You, the experienced spinner, can change it to suit yourself.
Here's a nice new bobbin with hardly any yarn on it. I stopped about every 30 seconds to move the slider just a little bit to get a thin layer of yarn on the bobbin core. I'm making the first layer as thin as I can stand to do because it is the base for everything else to follow. Yarn is much more likely to slide around in the first layer because the bobbin core is almost certainly some nice finished wood or hard plastic.
A fresh, nearly empty bobbin.
After the first layer, I can go a little longer before stopping to move the slider. But I still do it a lot, even with this fine yarn. You can already see that the second layer is thicker than the first. But it also contains more yarn because now the larger diameter takes a longer length for each wrap around. Every layer increases the diameter, which means you can spin longer before stopping to move it along. Small consolation for bulky spinners, but you can really tell the difference with fine yarn.
Winding the second layer.
Here's a full bobbin that has about 125g of yarn on it. That's around four and a half ounces and about as much as I can ever get on these standard Lendrum bobbins. I'm going to ply directly from this bobbin, because it was wound tightly and evenly I should have few problems getting it off. I can concentrate on plying, not fooling around with misbehaving bobbins.
A full bobbin.
One other thing to note: an evenly wound bobbin will hold as much of any particular yarn as possible, but different kinds of yarn fill up the bobbin faster or slower. Why? I can answer that with one word: Air. The more air in your yarn, the less yarn by weight you are going to get on the bobbin. You can get rid of that air either by spinning more dense yarn or by winding it on with a stronger tension or both, but that may not be what you want. It might not even be possible: some yarns will break before they get to the bobbin if you have too much tension. So that means that a bobbin of fluffy yarn is going to weigh less than a bobbin of hard twist smooth yarn. If you like to spin fluffy yarn, then you are really going to want to look at the size of the bobbins when you are shopping for a wheel.