If the moon is moving away at a distance of 1.48" per year (BBC), than wouldn't that mean the gravitational pull by the moon would weaken over time causing the tidal bulge to shrink? Thus causing sea levels to rise?
You are correct in saying that the moon is receding from the Earth. However, as you can see, this rate is very very small.
1.48 inches = 0.037592 meters
The Moon is 384400 kilometers away (on average), or 384400000 meters. That means every year, the Moon's distance increases by 0.00000000009779%. That's such a small difference, it is negligible on human timeframes.
Also, although the tides would shrink, this would not mean the sea level would rise. When we refer to rising sea levels, we refer to an average rise in sea levels that have been seen across the world, mostly due to climate change. During high tide, a beach may experience 4 meter higher sea level, but at low tide, it will experience 4 meter lower sea level. If the moon doubled its distance, then gravity would be a quarter its strength (gravity decreases with the square of the distance), so you would have 1 meter above during high tide and 1 meter below during low tide. As you can see, there is still no net change in sea level, it's just that the changes between high and low tide would be smaller. Again, this is negligible on human timeframes.