I've managed this year to more than triple my weekly centerfire shooting without increasing my budget. It requires a fair bit of investment for startup, but here's what I did:
Get a reloading setup, and load cast bullets. I'm loading .380, .45, .44 mag, and .308 for a half to a quarter of going price for factory stuff. The only reason the cost for some is as high as half is because I'm using higher quality bullets for better accuracy, or in the case of .308, I use cheap jacketed. (pulled surplus) Regardless, I got a more-than-basic setup, and it paid for itself inside two months.
If you're just shooting for groups or fun, print targets like others have suggested. If you're shooting for something specific (bullseye, etc) buy your targets in bulk. A big box of NRA bullseye target with run about $100, but it works out to about a penny a target.
Similar idea with ammo or components. Buy in bulk to get a better deal. Its more money up front, but its cheaper over time. Finding ammo/components can be tough right now, but its not impossible. Just look hard on the internet, sign up for back in stock notifications, get on backorder if you have to, and if possible, have friends outside your locale keep an eye out to increase your chances of finding something. I've been able to aquire all the primers, powder, etc, I've needed since the election, it just requires more time investment.
Join a club. It may seem like a lot of money at first, but if you look at it at cost per range trip, you'll start to see the savings. My range trips are costing me less than a dollar each now.
Get a shooting buddy or buddies. Split gas for trips to the range.
And of course, .22 is good as well. I enjoy it, but I don't see it as a replacement for centerfire, so I try to keep up with as much of that as I can.