The driftwood let it sink or on a safe angle so she can climb on it underwater and or sleep on it under water. Thats if its large enough to do that. Just not too close by basking area so she don’t hit it when diving into the water. Not overhead were it could fall and hit her. In water , let her play on it.
Don’t lower that heat bulb “under” the screen unsafe ! Yes will burn her since turtles are so curious to checking things out.
Try that 75 halogen bulb for the heat may work to reach the temp you need , if not the 90 try. If 90 to hot you can always raise it. You must have both bulbs over basking dock! When she get more comfortable with basking dock and her new home she will bask with you in the room. That takes more time !
Note : bulbs called basking bulbs are only heat for general reptiles. For turtles you also need that UVB “speciality bulb” to be adequate ! Both must be over dock. Use what you have now , later get into the ones that do both and only one fixture is cheaper. Mega Rays now make a small 70 watt which is great and last 18 months or longer producing usable UVB rays. Would work with your setup. I use this site : Self-Ballasted Lamps : ReptileUV, Products
Yes $46.95 but with loyalty code 25% off. You would have to buy three cheap ones to last as long as one Mega Rays making mega rays cheaper. Also not splash proof but they are "not" suppose to be that close anyway for placement ! 12-18" yes some even 20" or more so to spread out the UVB ray . Too low usable UVB ray would only be in an area about a few inches round serving no good. Read up on UVB placements , that site I gave has good info too ! And that link.
Crazy activity is good , that's normal for a turtle !
Keep basking area away from the side’s of the tank , turtles use it as a ladder to try and escape. Screen tops only help to prevent escape if clamped down. Turtles are very strong ! I use chop stick’s to space it away for safety. You may see how in my video , I think you may see it (just 2-3” out is enough). Another reason I don’t like glass tanks especially small ones, to narrow to do all truly need for safety. A good adult tank for her would be a 75-90 gallon part full or filled with an “ATBA”. You may want to Google above tank basking areas for the tank you have now then you could fill it all the way. Would buy you time before next upgrade. If you watch my video it a stock tank on the ground so to view from the top easy next to my chair. That’s so Piggley and I can play all the time.
Note what are you using to read the temp on basking area. Is it accurate ?
Also take notes will help you a lot. I'm old school and have 57 years of note books.