Going to the gym four times a week should be more than enough if you're eating properly. Especially if you focus on different muscle groups during different days.
Basically, my advice for anyone trying to bulk on a budget is to first try to get enough protein - depending on your height and weight, anywhere from 150g to 200g per day. After that, use the rest of your budget to get those calories. Find the cheapest source of carbs you can and buy that. Even though they have the most calories per gram, don't increase your daily fat intake by too much. For a 3000 calorie diet, your basic bulking spread could look something like this:
200 grams of protein = 800 calories
70 grams of fat = 630 calories
380 grams of carbs = 1520 calories
That's an example of what 2950 calories per day look like. Of course, individual's needs may vary - more protein, less fats, more or less carbs etc. Thus, for your particular issue, after you hit your daily protein requirement, use the rest of your cash on cheap foods that are rich in carbs. Just make sure not to go overboard. Don't worry about it too much however, even if you end up with more fat then you want, you will just need to work a bit harder during your next cut. As long as you're doing proper training and eating enough protein, your muscles will grow.