You've outlined the specific measures Allied air forces took against German jet fighters - bombing their airfields and attempting to catch them at low altitude around take-off and landing (sometimes known as "rat catching" or a "rat scramble"). In terms of protecting bombers in the air there was no particular change, the standard escort techniques combining free-ranging fighter sweeps in front of the bomber formations with closer protection from other fighter groups continued. US fighters had initially been instructed to stick closely to bomber formations, but from the start of 1944 were given increasing latitude to aggressively hunt and engage German fighters; the appearance of jet fighters did prompt a minor revision to orders, prohibiting escorts from dropping their external fuel tanks to speculatively pursue jets, as the difference in speed made such pursuits largely fruitless and forced the escort to turn for home early due to lack of fuel. German fighters of all types attacked unescorted bomber formations for preference so luring escorts away or forcing them to drop their tanks early could be considered a success, but this does not appear to have been a specific goal of Me 262 units.
Though the Me 262 possessed a clear speed advantage over the P-51 and could generally cut through escorts without being engaged, it was not entirely insurmountable; a US briefing outlined suggested tactics: "Advantage in speed of the 262 can be overcome by an advantage in altitude. By flying cover in stacked-up formations, with as much as 3,000 feet between flights, the upper element can reach a diving speed similar to the speed of an Me-262, and this can be exploited in attacking the jet, which needs from 9,000 to 12,000 feet for a split-S maneuver. Ideal situation for a P-51, for example, would result from a combination of two factors: first, speed gained through diving from superior altitude, making straight escape risky for the jet; second, exploiting its sluggishness in maneuvering if it should attempt an evasive turn." (USSAFE Air Intelligence Summary No. 76 for Week Ending 22 April 1945)
In general, though, Me 262s were never fielded in great enough numbers to have a significant impact on Allied strategy or tactics. The prospect of massed attacks was worrying, but lack of fuel, trained pilots and airfields meant it never transpired; "The spasmodic appearance of the jet was more of a scare than a real threat." (Development of the Long-Range Escort Fighter, US Air Force Historical Study No. 136).