The driver's license isn't all that unusual, I am a new agent and the standard office policy is never meet a new client at a property, always meet at the real estate office, or a public place, get a copy or picture of the license so that there is a record of the meeting. It really is a safety issue.
As far as buyer agent goes, perhaps figure out 2 or 3 prospective houses at a time, choose a day of the week where the agent has more availability (don't ask them to go to 3 100k houses on a Saturday afternoon for example, but maybe a Wednesday morning) to let them know you care about their time, show the agent you are serious, be it with your pre-approval letter or proof of downpayment funds. If they aren't interested in being your buyer agent, see if they can recommend a newer agent from their office that has more free time and could use the experience. Then you get the benefit of the agent you know being available for mentoring of the new agent so that key items aren't missed. If you are evaluating the property from an investor view point a buyer agent may not be valuing the property the same way your are so new or experienced doesn't matter much, your really just need someone willing to go to properties with you and put in offers.