Let's say I'm two miles away from entering the class B, heading straight for it at 1500 feet and climbing. Approach control gives me my clearance as "...cleared into the class Bravo at 3500 feet...". On one hand, they know my heading and altitude, so I assume that I should continue straight on, entering the Class B in my climb and level out at 3500 feet, which I have done often with no consequences. However, a very literal interpretation of the clearance would have me turn away and remain clear of the Class B until I had leveled at 3500, at which point I could turn back and enter it. If push ever came to shove, which interpretation is correct?
On one hand, they know my heading and altitude, so I assume that I should continue straight on, entering the Class B in my climb and level out at 3500 feet, which I have done often with no consequences.
This is what the controller wants you to do. It's slightly sloppy phraseology - "Cleared into Bravo, climb and maintain 3500" would be better. But what she said is not really ambiguous in any practical way. She would definitely not be expecting you to turn away, then climb, then turn back toward the B.
That's going to depend on your circumstances and previous clearances. Most likely it means you are cleared to enter a shelf of the class bravo airspace when your aircraft is at or above 3500' ASL.
Another interpretation is that you are cleared to enter a shelf of the class bravo with a floor at 3500', as listed on your charts. Check them before proceeding.
Another possibility is that the instruction is part of a procedure for a VFR transit route through the Class Bravo airspace which required the pilot, after establishing two way radio communications, to enter the Class Bravo airspace at a particular point, at a specific altitude then follow an established course through the class bravo under approach control. See the supplements for the Terminal Area Charts fro VFR through specific Class Bravo airspace.
But, yes the controller's instructions here are pretty vague. I've never heard an approach controller say anything like that.
You could respond with "Cleared into the Bravo, climbing to 3,500, Nxxxxx" for your clearance read back to make your intentions clear.
For example, I was flying from west of Boston to the northeast, under the Bravo and skirting north of a Class D, and asked approach for flight following, with higher when able. Approach asked if I wanted clearance into the Bravo at 5,500, I said yes. Then he cleared into Bravo, climb to 5000 and direct to destination (being /G is nice for that). Replied with 'cleared into Bravo, climb to 5,000, direct Pease (in this example), Nxxxxx'. No problem. I then continued to VFR at 5,500 after departing the Bravo and continuing northeast.