score:8
It's best for Cory Asbury himself to explain the meaning. From SongFacts website entry of his song:
"When I use the phrase, 'the reckless love of God,' I'm not saying that God Himself is reckless. I am, however, saying that the way He loves, is in many regards, quite so. His love bankrupted heaven for you. His love doesn't consider Himself first. His love isn't selfish or self-serving. He doesn't wonder what He'll gain or lose by putting Himself out there. He simply gives Himself away on the off-chance that one of us might look back at Him and offer ourselves in return.
The recklessness of His love is seen most clearly in this – it gets Him hurt over and over. Make no mistake, our sin pains His heart. Yet He opens up and allows us in every time. His love saw you when you hated Him – when all logic said, 'They'll reject me,' He said, 'I don't care if it kills me. I'm laying My heart on the line.'"
I have heard "reckless love" to be attributed to God's showing his love at the cross with vulnerability to be rejected but with invitation to feed those who see this horror at the cross as a mirror of one's sins being forgiven.
"reckless abandon" is another word commonly used to indicate overflowing liberality and generosity without caring for the danger of being disappointed when the excessiveness is not matched by commensurate return (i.e. unrequited love).
Guys who have fallen in love are familiar with this: they're not afraid to be embarrassed if their liberal display of singing under the window of his beloved with guitar, balloons, flowers, and backing vocals of his friends didn't win his girlfriend's heart but instead got ridiculed by others.
If you need another Biblical basis other than the Gospels, it's the book of Hosea.