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Recently the bulb for my turtle's heat lamp blew, will letting him outside to bask in the sun be sufficient enough until I get a new bulb?

How long will it take to get it? Outside basking is nice, but you don't need to do it often.

Its coming soon, but concerns I had were that he barely stays in the sun ling enough for it to be considered sunbathing, he kinda just wanders off and looks for a place to hide, also do ants pose a threat to turtles?, recently I've found that hes been getting himself into trouble with ants (digging into nests and just crossing paths with them in general)

Maybe you can take him out earlier in the day? Ants shouldn't pose a problem, though I'm not sure about nests. That could pose a problem and would be something to avoid.