There is convincing evidence that measures, like crushing the tablets before use, taking them with food or water, lower doses and temporary discontinuation of use, are associated with the lower risk of gastrointestinal bleeding.
DISCLAIMER: This information is not intended to interfere with any drug regime prescribed by a doctor.
How NSAIDs cause gastrointestinal bleeding?
According to Best Practice & Research: Clinical Gastroenterology, 2000:
NSAIDs can cause damage to the gastroduodenal mucosa via several
mechanisms, including the topical irritant effect of these drugs on
the epithelium, impairment of the barrier properties of the mucosa,
suppression of gastric prostaglandin synthesis, reduction of gastric
mucosal blood flow and interference with the repair of superficial
What can reduce the risk of bleeding?
1) Chewing the tablet and taking it with food or water:
Don't swallow the aspirin pill; chew it, and then swallow it with a
glass of water. Doing it that way gets the aspirin into your system
rapidly, which is what you want. (Harvard Medical School)
Chewing will break the tablet, making it to go through the stomach faster thus decreasing its erosive effect. Water will stimulate gastric emptying thus reducing the contact time of aspirin with gastric mucosa. Note, that milk or fruit juice will slow down gastric emptying. You can still take aspirin with food or with food and water. Food will slow gastric emptying of aspirin, but will dilute it. I don't know which is better, food or water, but both make sense.
2) Smaller doses of NSAIDs will be likely less erosive that the greater ones.
New formulations of NSAIDs may reduce risks of adverse events by using
lower doses while providing effective analgesia.
Lower-dose capsules that contain finely milled, rapidly absorbed NSAID
particles may also provide analgesia at lower systemic doses. (Drug, Healthcare and Patient Safety, 2015)
3) Topical NSAIDs reduce the risk of side effects:
Topical NSAIDs provided good levels of pain relief in acute conditions
such as sprains, strains and overuse injuries, probably similar to
that provided by oral NSAIDs. Gel formulations of diclofenac (as
Emugel®), ibuprofen, and ketoprofen, and some diclofenac patches,
provided the best effects. Adverse events were usually minimal. (Cochrane, 2015)
4) Temporary discontinuation of NSAIDs reduces the risk of GI bleeding:
All types and formulations of NSAIDs appear to increase the risk of
UGIBs [upper gastrointestinal bleedings] but the effect appear not to be cumulative and diminish rapidly
with discontinue of use. (British Journal of Clinical Pharmacology, 2002)
5) Vitamin C
Ascorbic acid supplementation has been associated with a decreased
incidence of bleeding from peptic ulcer disease and with a reduction
in NSAID-associated gastric mucosal damage. (Digestive Diseases and Sciences)
Aspirin + vitamin C tablets exist.
6 Foods to AVOID
7) Some NSAIDs are less often associated with GI bleeding than others:
According to the systematic review of studies Individual NSAIDs and Upper Gastrointestinal Complications (Drugs Safety, 2012), NSAIDs with the lowest risk of GI bleeding are aceclofenac, celecoxib and ibuprofen, and the ones with the highest risk are piroxicam, ketorolac and azapropazone (Fig. 2).
Using OTC drugs, such as sucralfate and antacides, sounds promising but was disappointing in reducing the risk of GI bleeding:
Despite promising results with sucralfate in smaller studies  or
for short-term prophylaxis [26, 31], a randomized, controlled trial
conduced by Agrawal and coworkers failed to show a significant benefit
of sucralfate in the prevention of gastric ulcers in contrast to
Data concerning antacids in the prevention of NSAID-related gastric
mucosal injury are scarce, and also disappointing. Especially for
long-term prophylaxis no clinical effect was observed with low-dose
antacids . (British Journal of Clinical Pharmacology, 2002)