It has a fuel filter and a carburetor. It is possible that fule is barely getting by the filter to fill up the float bowl in the carb at idle, however when more fuel is needed at higher speeds it if can not pump fuel fast enough through the clogged filter.
Another possibility is that the gas cap is not venting fast enough. The next time it starts to sound like it's going to die, pull over as fast and SAFE as possible so you don't die, then open the gas tank listen. If it hisses like a soda bottle does then the gas tank is not venting properly. Usallly the gas caps can be cleaned, in some cases they need to be replaced.
Most motorcycle shops don't keep parts for bikes over 10 years old. check ebay or bikebandit.com or even old junk yards. If you buy from a motorcycle grave yard don't pay more than 1/4 of what it cost new, becuase that one might have the same problem.
The fuel pumps usually keep it at a specific pressure. inside the carbs there are little "bowls" that store fuel as well. they work just like a toilet. a little thing floats in this bowl and keeps it at a constant consistant level, only opening when the bowl gets so low. I attached a picture of your carb for your bike so you can see what the float bowl looks like you can also go to
http://www.bikebandit.com/houseofmotorcycles/1997-honda-motorcycle-vt1100c-shadow/o/m9688#sch405015 to get any exploded diagram for your bike.
Item (4) is the bowl. Item (3) is the little plastic floaty thing that keeps the fuel at the right hight. in between those two cylinder things that look like two hockey pucks is a valve that will open when it needs fuel. the pump only comes on when this valve opens. If the pump makes noise when you first turn the key in the on position it's probably not your pump. Don't tear the carb apart unless you have a rebuild kit. gaskets and o rings are one time use only. Let me know if you have any more questions I put this in simple terms as I could because I don't know your experience level. I can go more in depth if you need.