Will you be shopping at all in between those big trips? Besides the big monthly trip, I do an irregular trip to the local grocery stores that total to no more than once a week. These are based on needs of perishables and wanting to cash in on sale items. Having done the bi-weekly trips for years in the past, I can say that works too but for optimum savings, you need to find some stores that offer good deals all the time.
Currently, I use Budget Map to set up categories for spending. The envelope system would work as well for you to put aside funds each check to build up to what you need for your grocery trip. I am trying to build up to being able to "hold" my funds to disperse them into categories only once a month. Then I can track what I spend in each and that's it for that month.
Stocking up is an important part to being able to go longer than a week or even two before shopping. If you are cutting out weekly trips all together then you will need to be able to eat and live from your stock for at least two weeks but I recommend more for just in case you are delayed in shopping. You will need to look at non perishable options for foods too..canned, powdered, dehydrated or frozen and buy perishables only in quantities that can be eaten before they expire. If you plan to make a small perishables only run in between then be sure you stick to that...go directly to those aisles, don't browse and don't stop anywhere else.
Making use of coupons and sales. Even bi-weekly shopping can offer the use of these savings but you won't get the best deals on everything. You will need to check the sales for the day you shop and look for places that offer every day lower prices to take advantage of. If you plan to do a small weekly stop for perishables and sales then follow the above, set a budget for what you will spend weekly on this small trip and check the sales to stay within that amount. Don't buy anything but what is on your list of sale items and perishables.
Meal planning is essential. You need a well stocked kitchen with all the basics on hand. I do a mix of meal planning based on what is on hand and buying a few ingredients to make meals. I buy meats when I do make a small trip into town, these are not for immediate consumption but will be on hand for determining meals in the next "cycle". I meal plan before I go shopping. I can base these on what I have on hand while adding items I will need to complete meals to the list. I do stay within my budget for this. Eventually I hope to get that quarter of beef and some other meat sources that stock me up where I can stop shopping at the grocery store for the sales.