bottle_consumer.rb

class BottleConsumer
  attr_accessor :bottles, :caps, :dollars, :empty, :bottles_returned, :caps_returned

  def initialize(dollars) 
    @bottles = 0
    @caps = 0
    @empty = 0
    @dollars = dollars
    @caps_returned = 0
    @bottles_returned = 0
  end  
  
end

poppin_bottles.rb

require_relative 'bottle_consumer'

class BottleReturn

  def purchase_bottle
    while @consumer.dollars >= 2
      @consumer.bottles += 1
      @consumer.dollars -= 2
    end  
  end

  def drink_bottles
    while @consumer.bottles > 0
      @consumer.bottles -= 1
      @consumer.empty += 1
      @consumer.caps += 1
    end
  end   

  def return_bottles
    while @consumer.empty >= 2
      @consumer.empty -= 2
      @consumer.bottles += 1
      @consumer.bottles_returned += 1
    end  
  end

  def return_caps
    while @consumer.caps >= 4
      @consumer.caps -= 4
      @consumer.bottles += 1
      @consumer.caps_returned += 1
    end
  end

  def shop_cycle
    while @consumer.bottles > 0 
      drink_bottles
      return_bottles
      return_caps
    end  
    @consumer.bottles
  end 

  def run_program
    puts "Enter dollar amount you will spend: "
    dollars = gets.chomp.to_i
    @consumer = BottleConsumer.new(dollars)
    purchase_bottle
    shop_cycle
    puts "If you make an investment of $#{dollars} you will get back #{@consumer.caps_returned} bottles from returning the caps, and #{@consumer.bottles_returned} bottles from returning the empties. "
    puts "There will be #{@consumer.caps} caps remaining, and #{@consumer.empty} empty bottles left."
    restart_program
  end

  def restart_program
    restart = BottleReturn.new
    restart.run_program
  end  

end

start = BottleReturn.new
start.run_program
  

Love the fact that you did this in OOP!
You did a great job naming the methods as well.
Be careful with restart_program. You actually are creating a new program and running it, not restarting it. You want something like:

def restart_program
  run_program
end