It comes down to what you mean by “essentials”. Do you have any camping gear like a tent, sleeping bag or pad?
If you are looking to get some basic camping gear and a bunch of bikepacking bags, then you’ll be kind of limited by $150. A lightweight sleeping bag and pad could easily cost more. Your trip will also determine what kind of gear you need. A winter trip to the snowy woods will require a different setup than a hut-to-hut type of summer trip. Where and when do you plan on taking your trip?
Check out Bikepacking.com Bikepacking 101. They’ve got a few tips for getting started and how you can use dry bags and/or stuff sacks in place of bikepacking specific bags. If your bike has rear rack mounts, then the Topeak Explorer Rack might be a decent choice since you could secure a good sized stuff sack full of heavy gear on top with long strap. Another dry bag, like these fairly inexpensive ones with a couple more straps and you could secure a Marmot Voyager 55 Sleeping bag and a Therm-a-rest Trail Scout sleeping pad to the handlebars. There are tons of cheaper options, but those are just a couple choices from reputable brands.
The 10 essentials: first aid kit, water, food, light, shelter etc all become just a bit trickier when you have to carry them on a bike. Make sure you have the tools and replacement parts for any bike repairs that could leave you stranded with a long walk home. Regardless of your gear choices, a short shakedown trip close to civilization is always a good idea to help dial in your set up. If you’ve never camped before, I would also suggest a car camping trip to practice using your stove and setting up your tent etc.